ConvertingDecimalValuesintoBina ry,andViceVersa. PartA Being able to convert decimal values to binary (and vice versa) is very important in networking because this is the basis for how subnetting is done. You may have done some
of these exercises in high school and probably didn’t know why it was important to be able to convert decimal values into binary, and vice versa. This hands-on activity will help yourecallhowthisisdoneorwillteachhowtodoitincase youneverseenthisbefore.
152 Chapter 5 Network and Transport Layers
As you know, an IPv4 address consists of 32 bits that have been separated into 4 bytes (sometimes called octets), for example, 129.79.126.1. This is called the dotted decimal address. Each byte has 8 bits, and each of these bits can assumeavalueof0or1.Thefollowingtableshowshowwe converteachbinarypositiontoadecimalvalue:
Binaryposition 27 26 25 24 23 22 21 20 Decimalvalue 128 64 32 16 8 4 2 1
To practice the conversion from binary to decimal, let’s doacoupleproblemstogether: 1. You have the following binary number: 10101010. Convertitintodecimal. 10101010=(1 ∗ 128)+(0 ∗ 64)+(1 ∗ 32) +( 0 ∗ 16)+(1 ∗ 8)+(0 ∗ 4) +( 1 ∗ 2)+(0 ∗ 1)=128 +31+8+2 = 170 2. You have the following binary number: 01110111. Convertitintodecimal. 01110111=(0×128)+(1 ∗ 64)+(1 ∗ 32) +( 1 ∗ 16)+(0 ∗ 8)+(1 ∗ 4) +( 1 ∗ 2)+(1 ∗ 1) =64+32+16+4+2+1 = 119 Itisimportanttonoticewhattherangeofpossibledecimal values for each byte is. The lower bound is given when each bit is 0 and the upper bound is when each bit is 1. So 00000000willgiveus0and11111111willgiveus255.This isthereasonwhyIPv4addressescannotgoabovethevalue of255. Deliverable Calculate the decimal values of the following binary numbers:11011011,01111111,10000000,11000000,11001101. PartB Nowlet’spracticetheconversionofdecimalvaluetobinary. This is a bit trickier. Start by finding the highest binary
position that is equal to or smaller than the decimal number we are converting. All the other placeholders to the left of this number will be 0. Then subtract the placeholder value from the number. Then find the highest binary position that is equal to or smaller than the remainder. Keep repeating these steps until the remainder is 0. Now, let’s practice. 3. Convert60intoabinarynumber. a. Theplaceholderthatisequaltoorlowerthan60is 32.Therefore,thefirsttwobitsfor60are0andthe third one is 1 − 001_ _ _ _ _ . The next step is to subtract32from60,whichequals60−32 = 28. b. The placeholder that is equal to or lower than 32 is 16, which is the fourth bit from the left. Therefore, our binary number will look like this: 0011_ _ _ _. The next step is to subtract 16 from 28,whichequals28−16 = 12. c. Theplaceholderthatisequaltoorlowerthan12is 8, and this is the fifth bit from the left. Therefore, ourbinarynumberwilllooklikethis:00111___. Thenextstepistosubtract8from12,whichequals 12−8 = 4. d. The placeholder that is equal to or lower than 4 is 4, andthisisthesixth bitfromtheleft. Therefore, our binary number will look like this: 001111_ _. Thenextstepistosubtract4from4,whichequals 4−4 = 0. e. Given that our remainder is 0, the additional bits are0,andwefindthatouranswer:60inbinaryis 00111100. 4. Convert182intoabinarynumber. 182=10110110 (Because182−128 = 54,54−32 = 22,22−16 = 6, and6−4 = 2)
Deliverable Calculate the binary value for each of the following binary numbers:126,128,191,192,223

Use induction to solve the problem. Can you show me the steps too? I don't understand how to solve this.

3+4+5+...+(n+2)=1/2n(n+5)

1+5+5²+...+5^(n-1)=1/4(5ⁿ-1)

The Conch Café, located in Gulf Shores, Alabama, features casual lunches with a great view of the Gulf of Mexico. To accommodate the increase in business during the summer vacation season, Fuzzy Conch, the owner, hires a large number of servers as seasonal help. When he interviews a prospective server, he would like to provide data on the amount a server can earn in tips. He believes that the amount of the bill and the number of diners are both related to the amount of the tip. He gathered the following sample information.

CustomerAmount of TipAmount of BillNumber of DinersCustomerAmount of TipAmount of BillNumber of Diners

  Click here for the Excel Data File

a-1. Develop a multiple regression equation with the amount of tips as the dependent variable and the amount of the bill and the number of diners as independent variables and complete the table. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

a-2. Write out the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

a-3. How much does another diner add to the amount of the tips? (Round your answer to 2 decimal places.)

b. According to the p-values, which variable should be deleted if alpha = 0.05?

1. Calculate and interpret the three aspects of Descriptive Analysis for weekly return: Location, Shape and Spread. Hint: make sure you interpret these measures in the context of the data and pay attention to the unit of measurement in Excel.

2. Date	Weekly Return BIT
   11/3/13	-46.16
   18/3/13	-0.01
   25/3/13	39.23
   1/4/13	13.07
   8/4/13	23.93
   15/4/13	41.36
   22/4/13	26.5
   29/4/13	20.39
   6/5/13	25.5
   13/5/13	42.52
   20/5/13	37.88001
   27/5/13	15.66
   3/6/13	20.98
   10/6/13	25.28
   17/6/13	11.97
   24/6/13	-2.46
   1/7/13	14.95
   8/7/13	-3.5
   15/7/13	-8
   22/7/13	-0.05
   29/7/13	25.49
   5/8/13	4.099998
   12/8/13	9.529999
   19/8/13	58.75
   26/8/13	36.12
   2/9/13	47.87
   9/9/13	43.09
   16/9/13	42.08
   23/9/13	40.24001
   30/9/13	51.77
   7/10/13	93.52
   14/10/13	113.89
   21/10/13	133.5
   28/10/13	231.05
   4/11/13	447.08
   11/11/13	874.55
   18/11/13	1091.99
   25/11/13	916.27
   2/12/13	927.8199
   9/12/13	681.78
   16/12/13	789.11
   23/12/13	899
   30/12/13	937.92
   6/1/14	877.1
   13/1/14	900
   20/1/14	828.99
   27/1/14	750
   3/2/14	640
   10/2/14	628.37
   17/2/14	550
   24/2/14	574.73
   3/3/14	569.53
   10/3/14	546.83
   17/3/14	460
   24/3/14	418.31
   31/3/14	375
   7/4/14	467.54
   14/4/14	369
   21/4/14	402.16
   28/4/14	356
   5/5/14	410.9
   12/5/14	548.66
   19/5/14	652.71
   26/5/14	650
   2/6/14	571.71
   9/6/14	590
   16/6/14	565
   23/6/14	561.2
   30/6/14	592.14
   7/7/14	514.12
   14/7/14	500.84
   21/7/14	565.93
   28/7/14	587.76
   4/8/14	484.97
   11/8/14	443
   18/8/14	410.53
   25/8/14	437.92
   1/9/14	462.43
   8/9/14	324.44
   15/9/14	360.15
   22/9/14	253.36
   29/9/14	381.64
   6/10/14	385.55
   13/10/14	349.98
   20/10/14	319.9
   27/10/14	340.98
   3/11/14	363.96
   10/11/14	348.09
   17/11/14	371.5
   24/11/14	376
   1/12/14	319.55
   8/12/14	334.97
   15/12/14	343.46
   22/12/14	262.8
   29/12/14	250.09
   5/1/15	190.02
   12/1/15	380.51
   19/1/15	189.48
   26/1/15	209.59
   2/2/15	223.9
   9/2/15	223.5
   16/2/15	254.85
   23/2/15	251.34
   2/3/15	305.86
   9/3/15	249.82
   16/3/15	280
   23/3/15	220.56
   30/3/15	279.94
   6/4/15	265
   13/4/15	200
   20/4/15	224.68
   27/4/15	195.91
   4/5/15	245.03
   11/5/15	227.36
   18/5/15	269.69
   25/5/15	228.8
   1/6/15	220.5
   8/6/15	212.87
   15/6/15	225.62
   22/6/15	262.18
   29/6/15	343.58
   6/7/15	312.15
   13/7/15	301.96
   20/7/15	315
   27/7/15	262.04
   3/8/15	229.08
   10/8/15	257.53
   17/8/15	220.4
   24/8/15	249.46
   31/8/15	230.8
   7/9/15	223.27
   14/9/15	246.48
   21/9/15	250.66
   28/9/15	239.59
   5/10/15	273.53
   12/10/15	300.01
   19/10/15	377.69
   26/10/15	451.39
   2/11/15	371.79
   9/11/15	376.89
   16/11/15	418.39
   23/11/15	440.58
   30/11/15	505.46
   7/12/15	516.24
   14/12/15	481.21
   21/12/15	482.38
   28/12/15	542.2
   4/1/16	454.28
   11/1/16	473.92
   18/1/16	432.58
   25/1/16	429.39
   1/2/16	467.05
   8/2/16	509.61
   15/2/16	506.68
   22/2/16	448.07
   29/2/16	443.69
   7/3/16	484.58
   14/3/16	489.97
   21/3/16	485.82
   28/3/16	455.66
   4/4/16	474.93
   11/4/16	516.19
   18/4/16	488.28
   25/4/16	555.87
   2/5/16	542.67
   9/5/16	512.75
   16/5/16	601.27
   23/5/16	688.69
   30/5/16	803.09
   6/6/16	953.05
   13/6/16	805.65
   20/6/16	797.08
   27/6/16	771.54
   4/7/16	795.01
   11/7/16	793.52
   18/7/16	723.18
   25/7/16	687.93
   1/8/16	650.5
   8/8/16	660
   15/8/16	670
   22/8/16	715.6
   29/8/16	714
   5/9/16	734.99
   12/9/16	686.2
   19/9/16	719.42
   26/9/16	715.57
   3/10/16	754
   10/10/16	761.02
   17/10/16	825
   24/10/16	825.83
   31/10/16	831.9
   7/11/16	900.52
   14/11/16	902.97
   21/11/16	924.27
   28/11/16	975.2
   5/12/16	1006.2
   12/12/16	1135.94
   19/12/16	1281.4
   26/12/16	1144.41
   2/1/17	995.16
   9/1/17	1123.2
   16/1/17	1138.34
   23/1/17	1247.74
   30/1/17	1241.48
   6/2/17	1275.95
   13/2/17	1453.46
   20/2/17	1590.27
   27/2/17	1549.1
   6/3/17	1262.27
   13/3/17	1177.61
   20/3/17	1372.88
   27/3/17	1512.83
   3/4/17	1488.75
   10/4/17	1583.46
   17/4/17	1681.71
   24/4/17	2096.67
   1/5/17	2495.07
   8/5/17	2760.85
   15/5/17	2994.79
   22/5/17	3393.27
   29/5/17	3789.46
   5/6/17	3488.86
   12/6/17	3403.31
   19/6/17	3242.76
   26/6/17	3315.51
   3/7/17	2410
   10/7/17	3441.5
   17/7/17	3429.74
   24/7/17	3960.53
   31/7/17	5218.14
   7/8/17	5198.76
   14/8/17	5520
   21/8/17	5918.4
   28/8/17	5219.46
   4/9/17	4493.05
   11/9/17	4525.38
   18/9/17	5465.36
   25/9/17	5787.35
   2/10/17	7126.76
   9/10/17	7613.93
   16/10/17	7918.65
   23/10/17	9592.39
   30/10/17	7824.89
   6/11/17	10593.55
   13/11/17	12197.99
   20/11/17	14924.19
   27/11/17	21084.87
   4/12/17	25886.55
   11/12/17	18839.79
   18/12/17	18950.74
   25/12/17	22762.21
   1/1/18	18941.51
   8/1/18	15048.37
   15/1/18	14345.12
   22/1/18	10125.82
   29/1/18	10282.72
   5/2/18	13238.45
   12/2/18	12200.72
   19/2/18	14663.94
   26/2/18	12043.73
   5/3/18	10546.88
   12/3/18	10939.19
   19/3/18	8735.98
   26/3/18	9030.39
   2/4/18	10554.32
   9/4/18	11257.21
   16/4/18	12332.76
   23/4/18	12582.62
   30/4/18	11460.03
   7/5/18	11218.46
   14/5/18	9652.02
   21/5/18	10133.1
   28/5/18	8856.31
   4/6/18	8617.19
   11/6/18	8152.91
   18/6/18	8389.05
   25/6/18	8853.63
   2/7/18	8455.52
   9/7/18	9847.28
   16/7/18	11014.06
   23/7/18	9459.81
   30/7/18	8619.77
   6/8/18	8820.44
   13/8/18	9072.49
   20/8/18	9981.22
   27/8/18	8702.43
   3/9/18	8958.83
   10/9/18	9018.22
   17/9/18	9039.68
   24/9/18	9164.69
   1/10/18	8635.74
   8/10/18	8905.48
   15/10/18	8919.61
   22/10/18	8808.97
   29/10/18	8741.39
   5/11/18	7479.24
   12/11/18	5335.57
   19/11/18	5486.65
   26/11/18	4814.89
   3/12/18	4340.44
   10/12/18	5496.18
   17/12/18	5356.26
   24/12/18	5586.6
   31/12/18	4808.14
   7/1/19	4862.34
   14/1/19	4842.09
   21/1/19	4634.24
   28/1/19	5032.33
   4/2/19	4983.2
   11/2/19	5113.99
   18/2/19	5240.09
   25/2/19	5455.14
   4/3/19	5526.45
   11/3/19	5517.53
   18/3/19	5638.09
   25/3/19	7153.71
   1/4/19	7114.66
   8/4/19	7337.26
   15/4/19	7305.25
   22/4/19	8020.41
   29/4/19	9862.31
   6/5/19	11784.94
   13/5/19	12517.35
   20/5/19	12506.94
   27/5/19	10883.83
   3/6/19	12861.26
   10/6/19	15472.87
   17/6/19	15080.16
   24/6/19	16268.05
   1/7/19	14557.08
   8/7/19	14957.73
   15/7/19	13791.59
   22/7/19	16032.89
   29/7/19	16937.56
   5/8/19	15248.79
   12/8/19

1. Calculate the weekly return for BIT and construct a histogram in Excel. Does the data on return rates appear normally distributed? On the basis of z-scores do you find evidence of outliers? Hint: the formula for a return is (Current Price – Previous price)/Previous price multiplied by 100.

1. Calculate the weekly return for BIT and construct a histogram in Excel. Does the data on return rates appear normally distributed? On the basis of z-scores do you find evidence of outliers? Hint: the formula for a return is (Current Price – Previous price)/Previous price multiplied by 100.

2. Date	BIT
   11/3/13	52.06
   18/3/13	53.84
   25/3/13	99.99
   1/4/13	139.23
   8/4/13	113.07
   15/4/13	123.93
   22/4/13	141.36
   29/4/13	126.5
   6/5/13	120.39
   13/5/13	125.5
   20/5/13	142.52
   27/5/13	137.88
   3/6/13	115.66
   10/6/13	120.98
   17/6/13	125.28
   24/6/13	111.97
   1/7/13	97.54
   8/7/13	114.95
   15/7/13	96.5
   22/7/13	92
   29/7/13	99.95
   5/8/13	125.49
   12/8/13	104.1
   19/8/13	109.53
   26/8/13	158.75
   2/9/13	136.12
   9/9/13	147.87
   16/9/13	143.09
   23/9/13	142.08
   30/9/13	140.24
   7/10/13	151.77
   14/10/13	193.52
   21/10/13	213.89
   28/10/13	233.5
   4/11/13	331.05
   11/11/13	547.08
   18/11/13	974.55
   25/11/13	1191.99
   2/12/13	1016.27
   9/12/13	1027.82
   16/12/13	781.78
   23/12/13	889.11
   30/12/13	999
   6/1/14	1037.92
   13/1/14	977.1
   20/1/14	1000
   27/1/14	928.99
   3/2/14	850
   10/2/14	740
   17/2/14	728.37
   24/2/14	650
   3/3/14	674.73
   10/3/14	669.53
   17/3/14	646.83
   24/3/14	560
   31/3/14	518.31
   7/4/14	475
   14/4/14	567.54
   21/4/14	469
   28/4/14	502.16
   5/5/14	456
   12/5/14	510.9
   19/5/14	648.66
   26/5/14	752.71
   2/6/14	750
   9/6/14	671.71
   16/6/14	690
   23/6/14	665
   30/6/14	661.2
   7/7/14	692.14
   14/7/14	614.12
   21/7/14	600.84
   28/7/14	665.93
   4/8/14	687.76
   11/8/14	584.97
   18/8/14	543
   25/8/14	510.53
   1/9/14	537.92
   8/9/14	562.43
   15/9/14	424.44
   22/9/14	460.15
   29/9/14	353.36
   6/10/14	481.64
   13/10/14	485.55
   20/10/14	449.98
   27/10/14	419.9
   3/11/14	440.98
   10/11/14	463.96
   17/11/14	448.09
   24/11/14	471.5
   1/12/14	476
   8/12/14	419.55
   15/12/14	434.97
   22/12/14	443.46
   29/12/14	362.8
   5/1/15	350.09
   12/1/15	290.02
   19/1/15	480.51
   26/1/15	289.48
   2/2/15	309.59
   9/2/15	323.9
   16/2/15	323.5
   23/2/15	354.85
   2/3/15	351.34
   9/3/15	405.86
   16/3/15	349.82
   23/3/15	380
   30/3/15	320.56
   6/4/15	379.94
   13/4/15	365
   20/4/15	300
   27/4/15	324.68
   4/5/15	295.91
   11/5/15	345.03
   18/5/15	327.36
   25/5/15	369.69
   1/6/15	328.8
   8/6/15	320.5
   15/6/15	312.87
   22/6/15	325.62
   29/6/15	362.18
   6/7/15	443.58
   13/7/15	412.15
   20/7/15	401.96
   27/7/15	415
   3/8/15	362.04
   10/8/15	329.08
   17/8/15	357.53
   24/8/15	320.4
   31/8/15	349.46
   7/9/15	330.8
   14/9/15	323.27
   21/9/15	346.48
   28/9/15	350.66
   5/10/15	339.59
   12/10/15	373.53
   19/10/15	400.01
   26/10/15	477.69
   2/11/15	551.39
   9/11/15	471.79
   16/11/15	476.89
   23/11/15	518.39
   30/11/15	540.58
   7/12/15	605.46
   14/12/15	616.24
   21/12/15	581.21
   28/12/15	582.38
   4/1/16	642.2
   11/1/16	554.28
   18/1/16	573.92
   25/1/16	532.58
   1/2/16	529.39
   8/2/16	567.05
   15/2/16	609.61
   22/2/16	606.68
   29/2/16	548.07
   7/3/16	543.69
   14/3/16	584.58
   21/3/16	589.97
   28/3/16	585.82
   4/4/16	555.66
   11/4/16	574.93
   18/4/16	616.19
   25/4/16	588.28
   2/5/16	655.87
   9/5/16	642.67
   16/5/16	612.75
   23/5/16	701.27
   30/5/16	788.69
   6/6/16	903.09
   13/6/16	1053.05
   20/6/16	905.65
   27/6/16	897.08
   4/7/16	871.54
   11/7/16	895.01
   18/7/16	893.52
   25/7/16	823.18
   1/8/16	787.93
   8/8/16	750.5
   15/8/16	760
   22/8/16	770
   29/8/16	815.6
   5/9/16	814
   12/9/16	834.99
   19/9/16	786.2
   26/9/16	819.42
   3/10/16	815.57
   10/10/16	854
   17/10/16	861.02
   24/10/16	925
   31/10/16	925.83
   7/11/16	931.9
   14/11/16	1000.52
   21/11/16	1002.97
   28/11/16	1024.27
   5/12/16	1075.2
   12/12/16	1106.2
   19/12/16	1235.94
   26/12/16	1381.4
   2/1/17	1244.41
   9/1/17	1095.16
   16/1/17	1223.2
   23/1/17	1238.34
   30/1/17	1347.74
   6/2/17	1341.48
   13/2/17	1375.95
   20/2/17	1553.46
   27/2/17	1690.27
   6/3/17	1649.1
   13/3/17	1362.27
   20/3/17	1277.61
   27/3/17	1472.88
   3/4/17	1612.83
   10/4/17	1588.75
   17/4/17	1683.46
   24/4/17	1781.71
   1/5/17	2196.67
   8/5/17	2595.07
   15/5/17	2860.85
   22/5/17	3094.79
   29/5/17	3493.27
   5/6/17	3889.46
   12/6/17	3588.86
   19/6/17	3503.31
   26/6/17	3342.76
   3/7/17	3415.51
   10/7/17	2510
   17/7/17	3541.5
   24/7/17	3529.74
   31/7/17	4060.53
   7/8/17	5318.14
   14/8/17	5298.76
   21/8/17	5620
   28/8/17	6018.4
   4/9/17	5319.46
   11/9/17	4593.05
   18/9/17	4625.38
   25/9/17	5565.36
   2/10/17	5887.35
   9/10/17	7226.76
   16/10/17	7713.93
   23/10/17	8018.65
   30/10/17	9692.39
   6/11/17	7924.89
   13/11/17	10693.55
   20/11/17	12297.99
   27/11/17	15024.19
   4/12/17	21184.87
   11/12/17	25986.55
   18/12/17	18939.79
   25/12/17	19050.74
   1/1/18	22862.21
   8/1/18	19041.51
   15/1/18	15148.37
   22/1/18	14445.12
   29/1/18	10225.82
   5/2/18	10382.72
   12/2/18	13338.45
   19/2/18	12300.72
   26/2/18	14763.94
   5/3/18	12143.73
   12/3/18	10646.88
   19/3/18	11039.19
   26/3/18	8835.98
   2/4/18	9130.39
   9/4/18	10654.32
   16/4/18	11357.21
   23/4/18	12432.76
   30/4/18	12682.62
   7/5/18	11560.03
   14/5/18	11318.46
   21/5/18	9752.02
   28/5/18	10233.1
   4/6/18	8956.31
   11/6/18	8717.19
   18/6/18	8252.91
   25/6/18	8489.05
   2/7/18	8953.63
   9/7/18	8555.52
   16/7/18	9947.28
   23/7/18	11114.06
   30/7/18	9559.81
   6/8/18	8719.77
   13/8/18	8920.44
   20/8/18	9172.49
   27/8/18	10081.22
   3/9/18	8802.43
   10/9/18	9058.83
   17/9/18	9118.22
   24/9/18	9139.68
   1/10/18	9264.69
   8/10/18	8735.74
   15/10/18	9005.48
   22/10/18	9019.61
   29/10/18	8908.97
   5/11/18	8841.39
   12/11/18	7579.24
   19/11/18	5435.57
   26/11/18	5586.65
   3/12/18	4914.89
   10/12/18	4440.44
   17/12/18	5596.18
   24/12/18	5456.26
   31/12/18	5686.6
   7/1/19	4908.14
   14/1/19	4962.34
   21/1/19	4942.09
   28/1/19	4734.24
   4/2/19	5132.33
   11/2/19	5083.2
   18/2/19	5213.99
   25/2/19	5340.09
   4/3/19	5555.14
   11/3/19	5626.45
   18/3/19	5617.53
   25/3/19	5738.09
   1/4/19	7253.71
   8/4/19	7214.66
   15/4/19	7437.26
   22/4/19	7405.25
   29/4/19	8120.41
   6/5/19	9962.31
   13/5/19	11884.94
   20/5/19	12617.35
   27/5/19	12606.94
   3/6/19	10983.83
   10/6/19	12961.26
   17/6/19	15572.87
   24/6/19	15180.16
   1/7/19	16368.05
   8/7/19	14657.08
   15/7/19	15057.73
   22/7/19	13891.59
   29/7/19	16132.89
   5/8/19	17037.56
   12/8/19	15348.79

1 Let f(x, y) = 4xy, 0 < x < 1, 0 < y < 1, zero elsewhere, be the joint probability density function(pdf) of X and Y . Find P(0 < X < 1/2 , 1/4 < Y < 1) , P(X = Y ), and P(X < Y ). Notice that P(X = Y ) would be the volume under the surface f(x, y) = 4xy and above the line segment 0 < x = y < 1 in the xy-plane.

2. Let X and Y be two discrete random variables and the joint probability mass function (joint distribution) of X and Y is given by the following table:

1 2 3 4 (X)

1 0.10 0.05 0.02 0.02

2 0.05 0.20 0.05 0.02

3 0.02 0.05 0.20 0.04

4 0.02 0.02 0.04 0.10

(Y)

(a) Find the marginal distribution of X, i.e. construct a table such as

Values of X 1 2 3 4

Probabilities ? ? ? ?

Repeat the same for Y .

(b) Are X and Y independent? Why or Why not?

3. Let X and Y have the following joint density f(x, y): f(x, y) = e^−x if x > 0 and 0 < y < 1, 0 otherwise 1

(a) What are the marginal distributions of X and Y ? In other words, find the density of X, given by fX(x), and the density of Y , given by fY (y).

(b) Are X and Y independent?

(c) What is P(X^2 > 25, Y < 0.5)?

Four mass–spring systems oscillate in simple harmonic motion. Rank the periods of oscillation for the mass–spring systems from largest to smallest.

m = 2 kg , k = 2 N/m

m = 2 kg , k = 4 N/m

m = 4 kg , k = 2 N/m

m = 1 kg , k = 4 N/m

STAR Co. provides paper to smaller companies whose volumes are not large enough to warrant dealing directly with the paper mill. STAR receives 100-feet-wide paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The demands for these widths vary from week to week. The following cutting patterns have been established:

Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 2(12) + 1(15) + 2(30) = 99 feet used resulting in 100-99 = 1 foot of trim loss). Demands this week are 5,670 12-foot rolls, 1,680 15-foot rolls, and 3,350 30-foot rolls. Develop an all-integer model that will determine how many 100-foot rolls to cut into each of the five patterns in order to meet demand and minimize trim loss (leftover paper from a pattern).

Optimal Solution:

Trim Loss:  feet

Year    Name    MinPressure_before      Gender_MF       Category        alldeaths
1950    Easy    958     1       3       2
1950    King    955     0       3       4
1952    Able    985     0       1       3
1953    Barbara 987     1       1       1
1953    Florence        985     1       1       0
1954    Carol   960     1       3       60
1954    Edna    954     1       3       20
1954    Hazel   938     1       4       20
1955    Connie  962     1       3       0
1955    Diane   987     1       1       200
1955    Ione    960     0       3       7
1956    Flossy  975     1       2       15
1958    Helene  946     1       3       1
1959    Debra   984     1       1       0
1959    Gracie  950     1       3       22
1960    Donna   930     1       4       50
1960    Ethel   981     1       1       0
1961    Carla   931     1       4       46
1963    Cindy   996     1       1       3
1964    Cleo    968     1       2       3
1964    Dora    966     1       2       5
1964    Hilda   950     1       3       37
1964    Isbell  974     1       2       3
1965    Betsy   948     1       3       75
1966    Alma    982     1       2       6
1966    Inez    983     1       1       3
1967    Beulah  950     1       3       15
1968    Gladys  977     1       2       3
1969    Camille 909     1       5       256
1970    Celia   945     1       3       22
1971    Edith   978     1       2       0
1971    Fern    979     1       1       2
1971    Ginger  995     1       1       0
1972    Agnes   980     1       1       117
1974    Carmen  952     1       3       1
1975    Eloise  955     1       3       21
1976    Belle   980     1       1       5
1977    Babe    995     1       1       0
1979    Bob     986     0       1       1
1979    David   970     0       2       15
1979    Frederic        946     0       3       5
1980    Allen   945     0       3       2
1983    Alicia  962     1       3       21
1984    Diana   949     1       2       3
1985    Bob     1002    0       1       0
1985    Danny   987     0       1       1
1985    Elena   959     1       3       4
1985    Gloria  942     1       3       8
1985    Juan    971     0       1       12
1985    Kate    967     1       2       5
1986    Bonnie  990     1       1       3
1986    Charley 990     0       1       5
1987    Floyd   993     0       1       0
1988    Florence        984     1       1       1
1989    Chantal 986     1       1       13
1989    Hugo    934     0       4       21
1989    Jerry   983     0       1       3
1991    Bob     962     0       2       15
1992    Andrew  922     0       5       62
1993    Emily   960     1       3       3
1995    Erin    973     1       2       6
1995    Opal    942     1       3       9
1996    Bertha  974     1       2       8
1996    Fran    954     1       3       26
1997    Danny   984     0       1       10
1998    Bonnie  964     1       2       3
1998    Earl    987     0       1       3
1998    Georges 964     0       2       1
1999    Bret    951     0       3       0
1999    Floyd   956     0       2       56
1999    Irene   987     1       1       8
2002    Lili    963     1       1       2
2003    Claudette       979     1       1       3
2003    Isabel  957     1       2       51
2004    Alex    972     0       1       1
2004    Charley 941     0       4       10
2004    Frances 960     1       2       7
2004    Gaston  985     0       1       8
2004    Ivan    946     0       3       25
2004    Jeanne  950     1       3       5
2005    Cindy   991     1       1       1
2005    Dennis  946     0       3       15
2005    Ophelia 982     1       1       1
2005    Rita    937     1       3       62
2005    Wilma   950     1       3       5
2005    Katrina 902     1       3       1833
2007    Humberto        985     0       1       1
2008    Dolly   963     1       1       1
2008    Gustav  951     0       2       52
2008    Ike     935     0       2       84
2011    Irene   952     1       1       41
2012    Isaac   965     0       1       5
2012    Sandy   945     1       2       159
                                        

Open Hurricane data.

SETUP: Is it reasonable to assume that average hurricane pressure for category 4 is different from that of category 1? Given the data, your job is to check if this assertion is indeed reasonable or not. HINT: Read Lecture 24.

19. What would be the correct Null-Hypothesis?

• a. Data related to two different categories should not be related.
• b. The population averages are equal.
• c. The slope of the regression line is equal to zero.
• d. None of these.

20. The P-value is 3.33E-09. What can be statistically concluded?

• a. We reject the Null Hypothesis.
• b. We accept the Null Hypothesis.
• c. We cannot reject the Null Hypothesis.
• d. None of these.

21. Write a one-line additional comment.

• a. We cannot conclude that data related to two different hurricane categories are related.
• b. We are confident that hurricanes with category 4 has different pressure than those of category 1.
• c. We cannot conclude that hurricanes with category 4 has lower pressure than those of category 1.
• d. None of these.