Question: (a) State the properties of a density function. (b) Contrast the properties of the expected value and variance operators. (c) Let X1 and X2 be

(a) State the properties of a density function.

(b) Contrast the properties of the expected value and variance operators.

(c) Let X1 and X2 be two independent random variables with the same mean μ and variance σ2. Derive the mean and variance of the function Y = 1/3X1 + 2/3X2.

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