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Shankar has four different sweaters to wear to work (call them, owing to lack of imagination, sweater 1, 2, 3 and 4 respectively). Every day he chooses any one of these with equal probability (so probability 1/4) independent across different days. Let X be the number of different sweaters Shankar work in the 5 day work week. So for example if the 5 day sweater sequence is (3, 3, 2, 4, 3), i.e Monday he wore 3, Tuesday also 3, Wednesday 2 etc then X = 3. Compute E(X) and var(X)..

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Shankar has four different sweaters to wear to work (call them, owing to lack of imagination, sweater 1, 2, 3 and 4 respectively). Every day he chooses any one of these with equal probability (so probability 1/4) independent across different days. Let X be the number of different sweaters Shankar work in the 5 day work week. So for example if the 5 day sweater sequence is (3, 3, 2, 4, 3), i.e Monday he wore 3, Tuesday also 3, Wednesday 2 etc then X = 3. Compute E(X) and var(X).

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  • 1. Shankar has four different sweaters to wear to work (call them, owing to lack of imagination, sweater 1, 2, 3 and 4 respectively). Every day he chooses any one of these with equal probability (so probability 1/4) independent across different days. Let X be the number of different sweaters Shankar work in the 5 day work week. So for example if the 5 day sweater sequence is (3, 3, 2, 4, 3), i.e Monday he wore 3, Tuesday also 3, Wednesday 2 etc then X = 3. Compute E(X) and var(X).