Some of the eggs at a market are sold in boxes of six. The number, X, of broken eggs in a box has the probability distribution given in the following table.

x 0 1 2 3 4 5 6

P (X=x) 0.8 0.14 0.03 0.02 0.01 0 0

(Find the expectation and variance of the number of unbroken eggs in a box)

Question

Lawrence Faulkner

Mathematics

10 October, 14:12

Some of the eggs at a market are sold in boxes of six. The number, X, of broken eggs in a box has the probability distribution given in the following table.

x 0 1 2 3 4 5 6

P (X=x) 0.8 0.14 0.03 0.02 0.01 0 0

(Find the expectation and variance of the number of unbroken eggs in a box)

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Ruchus · Answer 1

E (x) = Summation xp (x) = 0 (0.8) + 1 (0.14) + 2 (0.03) + 3 (0.02) + 4 (0.01) + 5 (0) + 6 (0) = 0.14 + 0.06 + 0.06 + 0.04 = 0.3

Variance = [ (0 - 0.3) ^2 * 0.8 + (1 - 0.3) ^2 * 0.14 + (2 - 0.3) ^2 * 0.03 + (3 - 0.3) ^2 * 0.02 + (4 - 0.3) ^2 * 0.01 + (5 - 0.3) ^2 * 0 + (6 - 0.3) ^2 * 0] = 0.072 + 0.0686 + 0.0867 + 0.1458 + 0.1369 = 0.51

Some of the eggs at a market are sold in boxes of six. The number, X, of broken eggs in a box has the probability distribution given in the following table.x 0 1 2 3 4 5 6P (X=x) 0.8 0.14 0.03 0.02 0.01 0 0(Find the expectation and variance of the number of unbroken eggs in a box)

Some of the eggs at a market are sold in boxes of six. The number, X, of broken eggs in a box has the probability distribution given in the following table.

x 0 1 2 3 4 5 6

P (X=x) 0.8 0.14 0.03 0.02 0.01 0 0

(Find the expectation and variance of the number of unbroken eggs in a box)