Question: 6. Let X be a discrete random variable with the set of possible values {x1, x2, . . . , xn}; X is called a

6. Let X be a discrete random variable with the set of possible values {x1, x2, . . . , xn};

X is called a discrete uniform random variable if

P(X=i) 1in. n

(a) Find E(X) and Var(X) for the special case, where P xi = i, 1 ≤ i ≤ n. Note that n i=1 i = n(n + 1)/2 and Pn i=1 i2 = n(n + 1)(2n + 1)/6.

(b) Let X be a random integer from the set {1, 2, . . .N}. Find E(X), Var(X), and σX.

P(X=i) 1in. n

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