Question

For a symmetric distribution with mean µ, the mean absolute deviation is the expected value MAD(X) = E(|X − µ|), of the absolute difference |X − µ|, which is strictly positive. The mean absolute deviation for the standard normal distribution is an integral 1 √ 2π Z ∞ −∞ |x| e −x 2/2 dx = p 2/π = 0.7979....

Part a: Find the MAD of the Bernoulli-1/2 distribution.

Part b: Find the MAD of the binomial distribution Bin(2, 1/2).

Part c: Find the mean absolute deviation of the normal distribution with variance 500?

Part d: Comment briefly on the relevance of the previous calculation to the number of heads in the Kerrich sequence.

Part e: True or false? MAD(3X + 7) = 3 × MAD(X).

Answer 1

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