Let Y be a discrete random variable with probability mass function p(y). Let k be a constant. Suppose p(y) = ky for y = 1; 2; 3; 4; 5. For any other...

1. Let Y be a discrete random variable with probability mass function p(y). Let k be a constant. Suppose p(y) = ky for y = 1; 2; 3; 4; 5. For any other values of y, p(y) = 0. Determine the value of k.

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2. A student randomly guesses on a five question multiple choice exam (and hence independence between each question can be assumed). The probability of correctly guessing each question is 0.2. Let X be the random variable for the number of correct guesses.

(i) Explain why this scenario follows a binomial probability model.(ii) Determine the probability of answering exactly 3 questions correctly.(iii) Determine the probability of answering at most 2 questions correctly.(iv) The mean and variance of a binomial random variable is = np and 2 = np(1 ???? p), respectively.Determine the mean and variance of X.