NOTE : 3(B) ,3(C) ,4(B),4(C),5(A),5(B) ARE WRONG . AS A PROOF I PASTED THERE Question 1: (3 points) Answers to the following questions should be calculated in Matlab and given to 4 decimal places.  Be careful not to introduce errors by rounding in any intermediate calculations as this may lead to an incorrect final answer. Suppose that the lifetime, T, for a certain type of disk drive follows an exponential distribution. (a) If it is given that 6% of drives fail within 2 years, find the parameter λ for the exponential distribution.  _____5.5466_____  (b) Find E(T).  _____5.5466_____ (c) Calculate the probability that the lifetime T for a randomly chosen disk drive exceeds 0.9 years.  _____3.3070*10^-7_____  Question 2: (2 points) Answers to the following questions should be calculated in Matlab and given to 4 decimal places.  Be careful not to introduce errors by rounding in any intermediate calculations as this may lead to an incorrect final answer. Suppose the discrete random variable X has the following probability distribution. x p(x) x1=3 p1=0.1 x2=4 p2=0.15 x3=7 p3=0.05 x4=9 p4=0.3 x5=12 p5=0.4 (a) Find E(X).  ____8.75______   Explanation: (b) Find var(X).  ____11.0875______  Question 3: (3 points) Answers to the following questions should be calculated in Matlab and given to 4 decimal places.  Be careful not to introduce errors by rounding in any intermediate calculations as this may lead to an incorrect final answer. In a certain workshop, the total cost, C for servicing a car is C=X+80Y where X is the cost of parts and Y is the time (in hours) taken to perform the service. Suppose, for a randomly chosen car, that X∼N(120,202) and Y∼N(2.6,0.52) independently. (a) Find E(C).  _____328_____  (b) Find var(C).  _____206.16_____  (c) Find the probability that the total cost of service, for a randomly chosen car, will be no more than $350.00.  _____0.9370_____  Probability = Question 4: (3 points) Answers to the following questions should be calculated in Matlab and given to 4 decimal places.  Be careful not to introduce errors by rounding in any intermediate calculations as this may lead to an incorrect final answer. Suppose that the diameters of particles in a sediment are distributed uniformly between 0.5 and 2.1 mm. Let D be the diameter of randomly chosen particle. (a) Find E(D).  ______1.3______  (b) Find the standard deviation sd(D).  _____0_____   0 since uniformly distributed (c) Find the proportion of particles with diameters between 0.6 and 0.9 mm.  ____0.0900______  Probability = Question 5: (2 points) Answers to the following questions should be calculated in Matlab and given to 4 decimal places.  Be careful not to introduce errors by rounding in any intermediate calculations as this may lead to an incorrect final answer. Let X and Y be independent random variables with variances 7 and 1 respectively and let Z=X+Y. (a) What is the value of cov(X,Z)?  ____ ...

1. NOTE : 3(B) ,3(C) ,4(B),4(C),5(A),5(B) ARE WRONG . AS A
PROOF I PASTED THERE
Question 1: (3 points)
Answers to the following questions should be calculated in
Matlab and given to 4 decimal places. Be careful not to
introduce errors by rounding in any intermediate calculations as
this may lead to an incorrect final answer.
Suppose that the lifetime, T, for a certain type of disk drive
follows an exponential distribution.
(a) If it is given that 6% of drives fail within 2 years, find the
parameter λ for the exponential distribution.
_____5.5466_____
(b) Find E(T).
_____5.5466_____
(c) Calculate the probability that the lifetime T for a randomly
chosen disk drive exceeds 0.9 years.
_____3.3070*10^-7_____

2. Question 2: (2 points)
Answers to the following questions should be calculated in
Matlab and given to 4 decimal places. Be careful not to
introduce errors by rounding in any intermediate calculations as
this may lead to an incorrect final answer.
Suppose the discrete random variable X has the following
probability distribution.
x
p(x)
x1=3
p1=0.1
x2=4
p2=0.15
x3=7
p3=0.05
x4=9
p4=0.3
x5=12
p5=0.4
(a) Find E(X).
____8.75______
Explanation:
(b) Find var(X).
____11.0875______

3. Question 3: (3 points)
Answers to the following questions should be calculated in
Matlab and given to 4 decimal places. Be careful not to
introduce errors by rounding in any intermediate calculations as
this may lead to an incorrect final answer.
In a certain workshop, the total cost, C for servicing a car is
C=X+80Y
where X is the cost of parts and Y is the time (in hours) taken to
perform the service. Suppose, for a randomly chosen car, that
X∼N(120,202)
and
Y∼N(2.6,0.52)
independently.
(a) Find E(C).
_____328_____
(b) Find var(C).
_____206.16_____
(c) Find the probability that the total cost of service, for a
randomly chosen car, will be no more than $350.00.

4. _____0.9370_____
Probability =
Question 4: (3 points)
Answers to the following questions should be calculated in
Matlab and given to 4 decimal places. Be careful not to
introduce errors by rounding in any intermediate calculations as
this may lead to an incorrect final answer.
Suppose that the diameters of particles in a sediment are
distributed uniformly between 0.5 and 2.1 mm. Let D be the
diameter of randomly chosen particle.
(a) Find E(D).
______1.3______
(b) Find the standard deviation sd(D).
_____0_____
0 since uniformly distributed
(c) Find the proportion of particles with diameters between 0.6
and 0.9 mm.
____0.0900______

5. Probability =
Question 5: (2 points)
Answers to the following questions should be calculated in
Matlab and given to 4 decimal places. Be careful not to
introduce errors by rounding in any intermediate calculations as
this may lead to an incorrect final answer.
Let X and Y be independent random variables with variances 7
and 1 respectively and let Z=X+Y.
(a) What is the value of cov(X,Z)?
______2.6457______
(b) What is the value of the correlation coefficient ρX,Z?
_____0.3780_____
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