Assignment:
Question 1:
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).
(b) Find var(C).
(c) Find the probability that the total cost of service, for a randomly chosen car, will be no more than $350.00.
Question 2:
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)?
(b) What is the value of the correlation coefficient ρX,Z?