Problem 6 Let X be a random variable with the following probability density function, fx(x)= [sin(x) 0xT otherwise Find the mean and variance of X. Problem 7 Find the mean and variance of the random variable X2 with the following distributions: (i) X~ N(,0) (ii) X ~ P(X) (iii) X~ exp(A) Problem 8 Find the mean and variance of the following random variables. (i) XGamma(a,) (ii) E(X)=,Var(X) =. Find mean and variance of Y = ax + b