1. [Compulsory] Let X be a Bernoulli random variable with pmf 1 -p if x =0 p(x) =P if x = 1. O if x # 0, 1 Compute (a) E(X) , (b) E(X2 ) , (c) V(X), (d) E(X30 ) 2. [Compulsory] Let X be a continuous random variable with pdf f ( x ) = k ( ( x - 3 ) 2 + 1 ) if 05 x 5 4 0 otherwise Find (a) the value of k , (b) P(X > 3) , (c) P(1X-3| >) 3. [Compulsory] A continuous random variable X has the following cdf: 1-(1+x)e * if x20 F(x) = 0 if x