Assume that the discrete random variable x can assume the values 1, 2, , n, and that those values are equally likely a Show that (n l) 2 b Show that 2 (n2 1) 12 c An experiment consists of randomly selecting a whole number between 1 and 50, and the random variable x is the value of the number selec...

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Assume that the discrete random variable x can assume the values 1, 2,..., n, and that those

Question:

Assume that the discrete random variable x can assume the values 1, 2,..., n, and that those values are equally likely.
a. Show that µ. = (n + l)/2.
b. Show that σ2 = (n2 - 1)/12.
c. An experiment consists of randomly selecting a whole number between 1 and 50, and the random variable x is the value of the number selected. Find the mean and standard deviation for x.