Consider the population described by the probability distribution shown in the table. The random variable x is observed twice. If these observations are independent, all the different samples of size 2 and their probabilities are shown in the accompanying table. Complete parts a through e below.

a.) Find the sampling distribution of s^2. Type the answers in ascending order for s^2

(type as integers or decimals)

b. Find the population variance:

c.) Find the sampling distribution of the sample standard deviation.

The following is the transition probability matrix of a Markov chain with states

1,2,3,4
⎛⎞

.4 .3 .2 .1 P=⎜.2 .2 .2 .4⎟ ⎝ .25 .25 .5 0 ⎠

.2 .1 .4 .3
(a) find the probability that state 3 is entered before state 4;

If X0 = 1
(b) find the mean number of transitions until either state 3 or state 4 is entered.

Is the percentage average room rate increase from May to August affected by the number of stars of a hotel? In order to answer this question you are asked to use one way analysis of variance. 1.1 Compute the percentage Average Room Rate Increase from May to August for each hotel in the sample, rounding up to the second decimal. Call this variable PCT_ARR_INCREASE. 1.2 State the null and alternative hypotheses.

We have 3 columns ARR_MAY(AVERAGE ROOM RATE MAY) ,ARR_AUG(AVERAGE ROOM RATE AUG) AND STARS

STARS   ARR_MAY   ARR_AUG
5   95   160
5   94   173
5   81   174
5   131   225
5   90   195
5   71   136
5   85   114
4   70   159
4   64   109
4   68   148
4   64   132
4   59   128
4   25   63
3   76   130
3   40   60
3   60   70
3   51   65
3   65   90
2   45   55
1   35   90
4   22   51
4   70   100
3   60   120
3   40   60
3   48   55
2   52   60
2   53   104
2   80   110
2   40   50
1   59   128
4   90   105
3   94   104
2   29   53
2   26   44
1   42   54
1   30   35
2   47   50
1   31   49
1   35   45
1   40   55
1   40   55
1   35   40
3   40   55
4   57   97
2   35   40
5   113   235
5   61   132
5   112   240
5   100   130
4   87   152
4   112   211
4   95   160
4   47   102
4   77   178
4   48   91
3   60   104
3   25   33
5   68   140
4   55   75
3   38   75
3   45   70
3   45   90
5   100   180
4   180   250
3   38   84
3   99   218
3   45   95
2   28   40
2   30   55
1   16   35
3   40   70
2   60   100
1   16   20
2   22   41
2   55   100
1   40   100
1   80   120
1   80   120
1   18   35
3   80   100
2   30   45
1   40   65
1   30   50
1   25   70
1   30   35
4   215   265
4   133   218
2   35   95
2   100   150
2   70   100
5   60   90
5   119   211
5   93   162
5   81   138
5   44   128
5   100   187
5   98   183
5   100   150
5   102   211
5   103   160
4   40   56
4   69   123
4   112   213
4   80   124
3   53   91
4   73   134
4   94   120
4   70   100
3   40   75
3   50   90
3   70   120
3   80   95
3   85   120
3   50   80
3   30   68
3   30   100
2   32   55
2   50   90
2   70   120
2   30   73
2   94   120
4   100   180
2   70   120
2   19   45
2   35   70
2   50   80
1   25   45
1   30   50
2   55   80
3   95   120
1   25   31
1   16   40
1   16   40
1   19   23
1   30   40

PLEASE ANSWER QUESTION 1.1 AND 1.2 THANKS IN ADVANCE

Q1,--Find median and mode of the 2 messages received on 9 consecutive days 15, 11, 9, 5, 18, 4, 15, 13, 17.
1-13, 18
2- 15, 16
3-18, 15
4-13, 6

Q2--A coin is thrown up 4 times. The probability that tails turn up in 3 cases is
1-none of the above
2- 1/3
3-1/2
4- 1/4

1 Two events are mutually exclusive if they cannot occur at the same time.

True

False

2.

An apartment building has the following apartments:

If an apartment is selected at random, what is the probability that it is not a 2 bedroom apartment on the 2nd floor?

Look at the data for the Japanese yen from 2000 to the present. Assume that you were in Tokyo for New Year’s Eve from January 1, 2010 to January 1 this year and bought a bento (box lunch) for 1000 yen each year. Convert this amount to dollars for the first day in January that data is available for each of the years you were in Tokyo.

1. Create a chart that plots the dollar price of the bento box overtime on each of the days in January you used.
2. Has the dollar appreciated or depreciated against the yen during this time period?
3. What the least amount in dollars that your box lunch cost ($ amount and date)?
4. What the most amount in dollars that your box lunch cost ($ amount and date)? please Make sure you calculate the US$ price of the bento box for every January between 2010 and the present. please no handwriting

3.         A teacher is interested in whether the number of bullying incidents by active bullies varies by class. The following data are the number of bullying incidents that occurred for 5 individuals randomly selected from 4 separate courses. Test the null hypothesis at the .01 level of significance that bullying does not vary across class. In so doing, identify: (1) the research and null hypothesis, (2) the critical value needed to reject the null, (3) the decision that you made upon analyzing the data, and (4) the conclusion you have drawn based on the decision you have made.

*Please show all work*

Let ? = {?1, ?2, ?3, … … … … ?? } ?? ? = {?1, ?2, ?3, … … … … ?? } Prove by induction that the number of injective functions ? from ? ?? ? is ?!

A study was performed comparing the efficacy of a new pain reliever, Galproxidone, to several pain relievers commonly prescribed after orthopedic surgury. Patients were asked to rate their pain after taking each medication. The data is listed below. Perform an ANOVA to determine the relative efficacy of Galproxidone on pain relief compared to the other pain relievers. If differences exist, perform a Bonferoni post-hoc test to determine which pain relievers are different from Galproxidone. Interpret the final results in terms of relative efficacy of the pain relievers.