Problem #2: Suppose a random variable X has expected value E[X] = 1 and variance Var(X) = 4. Compute the following quantities. (a) E[X + 3] (b) E[X2] (c) E[(X + 3)2] (d) Var[X + 1]Problem #3: Let Z~N(0, 1) and X ~ N(2, 9). (a) Calculate E[ZA]. (b) Calculate E[X ] (hint: try expressing X as a function of Z, and note E[Z"] = 0 whenever n is odd)Problem #4: We are throwing darts at a disk (i.e. a filled in circle) shaped board of radius 5. We assume that the position of the dart is a uniformly chosen point in the disk. The board has a disk shaped bullseye with radius 1. Suppose that we throw a dart 2400 times at the board. Estimate the probability that we hit the bullseye at least 84 times