1) A discrete random variable X has the following probability distribution:

Compute each of the following quantities (give the exact numbers):

(a) P(18)=

(b) P(X>18)=

(c) P(X?18)=

(d) The mean ? of X is

(e) The variance ?2 of X is (write all decimal points)

(f) The standard deviation ? of X is (use 4 decimal points)

2) Borachio works in an automotive tire factory. The number X of sound but blemished tires that he produces on a random day has the probability distribution

For the following, don’t round the numbers

(a) Find the probability that Borachio will produce more than three blemished tires tomorrow.

(b) Find the probability that Borachio will produce at most two blemished tires tomorrow.

(c) Compute the mean of X.

3)Find the mean ? and standard deviation ? of a random variable X with the following probability distribution

(a) ?=1.5, ?=0.96

(b) ?=1.2, ?=0.96

(c) ?=1.5, ?=0.98

(d) ?=1.2, ?=0.98

(e) ?=1.5, ?=2.4

4). To set a schedule for a new bus route, the transit authority repeatedly times the trip between two points; the time X in minutes is found to have the following probability distribution function

(a) the probability that a randomly selected trip will take at least 24 minutes is about:

(i) 0.14; (ii) 0.10; (iii) 0.23; (iv) 0.04; (v) 0.86

(b) The probability that a randomly selected trip will take between 21 and 24 minutes (including 21 and 24) is about: (i) 0.19; (ii) 0.79; (iii) 0.89; (iv) 0.29; (v) 0.7

(c) If the trip is made over and over, the average time it takes in minutes is about:

(i) 22.5; (ii) 22.2; (iii) 21.9; (iv) 22.0; (v) 23.0

5) A sociologist surveyed the households in a small town. The random variable X represents the number of dependent children in the households. The missing probability is

(a) 0.02

(b) 0.12

(c) 0.22

(d) 0.32

(e) 0.78

6) The following is a probability distribution function. True or False?

From the variable analysis above, provide the analysis and interpretation for three individual variables. This would include no more than 1 graph for each, one or two measures of central tendency and variability (as appropriate), the shapes of the distributions for quantitative variables, and two or three sentences of interpretation.

For the 10 pairings, identify and report only on three of the pairings, again using graphical and numerical summary (as appropriate), with interpretations. Please note that at least one pairing must include a qualitative variable and at least one pairing must not include a qualitative variable.

Format for report:

Brief Introduction

Discuss 1st individual variable, using graphical, numerical summary and interpretation

Discuss 2nd individual variable, using graphical, numerical summary and interpretation

Discuss 3rd individual variable, using graphical, numerical summary and interpretation

Discuss 1st pairing of variables, using graphical, numerical summary and interpretation

Discuss 2nd pairing of variables, using graphical, numerical summary and interpretation

Discuss 3rd pairing of variables, using graphical, numerical summary and interpretation

Conclusion

1) Alternative compiled code sequence using instructions in classes A, B, C. What is the average CPI of sequence 1 and sequence 2?

class A B C

CPI for class 3 4 6

IC in Sequence 1 6 12 10

IC in sequence 2 2 4 2

2) given the 8-bit binary number 1011 1110 (two's compliment, we will call this number N)

a) what is the hEX representation of N

b) what is the decimal value if N is an 8-bit 2's compliment signed number?(please write steps

c)what is the decimal value if N is an 8-bit unsigned number?

This game will play like this :

1) You start with $100

2) You roll a regular six-sided die:

{ 1 or 2  --> I multiply your money by 1/5 }

{ 3 or 4 --> I take all your money}

{ 5 or 6 --> I multiply your money by 6 }

3) With whatever money you have left, we repeat step (2) one more time

4) Then we stop

Find the expected amount of money you will have at the end of this game.

The data in the table is the number of absences for 7 students and their corresponding grade. Number of Absences 1 2 3 4 6 7 8 Grade 5 4.5 4 3.5 2.5 2 1

Step 1 of 3: Calculate the correlation coefficient, r. Round your answer to six decimal places. Step 2 of 3: Determine if r is statistically significant at the 0.01 level. Step 3 of 3: Calculate the coefficient of determination, r2 . Round your answer to three decimal places.

Use the normal equations to directly apply the least squares method (that is, do not use a transformation or Excel’s built in trendline function) to the given data for the indicated model. Compute D and dmax as bounds for cmax; what do these bounds suggest about improving the fit by using the Chebyshev criterion?

x 1 2 3 4 5

y 1 1 2 2 4

a. y = ax + b

b. y = ax2

Analyze the deviations for each model. Which model is a better fit? Support your conclusions

Answer the following question using the table below.

At what point does diminishing marginal utility set in?

If apples were freely given away at zero cost, how many apples would she choose to consume?

1. Explain how the antimicrobial bacteria are made

2. Medication to kill bacteria are produced to target a component in the bacterial cell.

List these targets

3. List 5 different classes of medication in microbials (bacterial, fungus and/or viruses) and explain the mechanism of action.

4. Find if these 5 medication are effective or not on these 3 bacteria. Please give a yay or nay.

1- Ecoli.

2- Mycobacterium smegmatis.

3- Staphylociccus Saprophyticus.

Medication

1- Chloramphenicol

2- Ethromycin

3-Penicillin G

4-Streptomycin

5- Tetracycline

Consider two Bonds: 1) a zero-coupon bond with face value F maturing in 1 year; 2) a coupon bond with face value F maturing in 4 years, i.e., T = 4, with coupon of $12 paid annually. Suppose that the continuous compounding is at the rate of r = 10%. (4a). If the price of bond 2 is equal to 1.15 times that of bond 1, find the face value F. (4b). If F = $100, how long will it take the value of bond 2 to reach $110 for the first time ?

1. Consider the following set of processes, with the length of CPU burst and arrival time given in milliseconds.                                                             

Process            Burst time       Priority            Arrival Time            

P₁                         10                    3                              0

P₂                          1                     1                              2

P₃                          2                     4                              4

P₄                          5                     2                              8

a)

Draw the Gantt chart that illustrates the execution of these processes using the preemptive priority scheduling algorithm (a smaller priority number implies a higher priority).

b)

What is the average waiting time for these processes using the preemptive priority scheduling algorithm?