Rods of length 2 m or 3 m are selected at random with probabilities 0.4 and 0.6

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Rods of length 2 m or 3 m are selected at random with probabilities 0.4 and 0.6 respectively.

(a) Find the expectation and variance of the length of a rod.

(b) Two lengths are now selected at random. Find the expectation and variance of the sum of the two lengths.

(c) Three lengths are now selected at random. Show that the probability distribution of Y, the sum of the three lengths, is. P(Y-y) 6 7 8 9 0.064 0.288 0.432 0.216 and find E(Y) and Var(Y). Comment on your results

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