Let X be discrete uniform random variable on C 2 1 0 1 2 so

Let X be discrete uniform random variable on C = {?2, ?1, 0, 1, 2}. (so X ? DUnif(C)). Find the support and PMF of each of the following, and sketch a graph of the PMF (5 points each): Y = X^2 , Z = X^3/2.

Solution

x = (-2,-1,0,1,2)

X is uniformly distributed.

Y can take values as 0,1 and 4

P(y=0) = 0.2

P(y=1) = 0.4

P(y=4) = 0.4

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z = x^3/2

Z cannot take real values as for -2 and -2 exponent 3/2 is not real.

PDF of Z cannot be drawn.