Let X1 , X2 , . X7 be a set of seven independent random variables, each

having the exponential distribution with the mean value of 1, 1/2 , 1/3 , ...,1/7 respectively.

(a) Find the expected value and standard deviation of their sum T

≡ X1 + X2 + ... + X7 .

(b) What is the probability that min(X1 , X2 , ..., X7 ) > 0.03?

(c) Find the kurtosis of X1 .

(d) Compute the expected value of X1^3 /(1+X2 ^2) .