Question

(2) (20 pts) Let U be a random variable following a uniform distribution on the interval [0,1 Let (a) Is X a random variable? Why or why not? (b) Calculate EX] analytically

Please show your works

Answer 1

a) here as we can see that X depends on a random variable U ; therefore X is a random variable cause randomness in U will be imposed on value of X.

b)

as we know that mean of U =E(U) =(a+b)/2 =(0+1)/2 =0.5

hence E(X)=E(2U+1)=2E(U)+1 =2*0.5+1

E(X)=2