Let x be the number of heads in two fair coin tosses


Question: Let X be the number of heads in two fair coin tosses. Suppose U has uniform distribution on (0, 1), independently of X.

a) find the density of X + U and sketch its graph.

b) Find an alternate distribution for U such that for any integer-valued random variable X independent of U, the graph of the density of X + U is simply the usual histogram of the distributions of X.

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Basic Statistics: Let x be the number of heads in two fair coin tosses
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