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Answer each of the questions in the space below. {Total mark: 2?]; 2 marks for each question] 1. Suppose X 2 Bin{n, p} with n = 15 and p = {1.4, Y N Poissonlipt} with p, = 21 X and Y are independent. What is Var{3X 21/ + s)? '2. Given a poisson random variable X , where the probabilityr of no events in a certain period of time is 0.13.53, nd it = E{X}. 3. Suppose the moment generating function of a random variable X is given by 3le {it} = (\".2631 + 0.8)\" . Find em). 2:r :1. Suppose X is an exponential random variable 1ivith probability density function {p.d.f.] fl. {32] = 2 e for 1' :5- D. 'What is P[X :- 5 I X :=- 3)? 5. Here are several scatterplots. The calculated correlations are -0.977, -0.021, 0.736, and 0.951. Match up the correlation coefficients with their corresponding scatterplots. (c) CI d: a: b:Questions 6, 7, 8 and 9 are based on the following joint probability function f(r, y) = P(X = x, Y = y) of random variables X and Y: f (I, y) 1 2 3 0 2k 0.1 0.3 y k 0.1 0.2 6. Find k. 7. What are the marginal probability functions of X and Y? 8. Let Z = X Y. Find the probability function of Z.E3. \"'hat is the covariance Cm.I{X._ Y]? ID. There are l cans of soup: T tomato and sun chicken. 1fou randomly choose 5 cans. Give an expression for the probability that exactlyr d1 of them are tomato. Evaluate this expression using a suitable approximation