Widgets are stored in boxes, and boxes are assembled in crates. Let X be the num

Question

Widgets are stored in boxes, and boxes are assembled in crates. Let X be the number of widgets in any particular box, let N be the number of boxes in any particular crate, and let K be the number of crates in any particular shipment. Assume that X, N, and K are independent integer-valued random variables, with expected value equal to 10, and variance equal to 16. Evaluate the expected value and variance of the following random variables.

a) The number of widgets in any particular crate.

b)The totla number of widgets in any particular shipment.

Explanation / Answer

X widgets in each of the N boxes in each of the K crates

a.) Number of widgets in a crate

Expected value = 10 NX

Expected variance = 16(NX)^2

b.) Total number of widgets

Expected value = 10NKX

Expected variance = 16(NKX)^2

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