The discussion focuses on determining the range and probability mass function (PMF) of the random variable Y, defined as Y = |X - 5|, where X follows a Geometric distribution with parameter p = 1/3. The PMF of X is given by P_X(k) = (1/3)(2/3)^(k-1) for k = 1, 2, 3, ... To find the PMF of Y, one must analyze the values of X that yield specific values of Y, such as Y = 0 and Y = 1, by solving the equations |X - 5| = k for various k.
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Jonobro said:Homework Statement
Let X∼Geometric(1/3), and let Y=|X−5|. Find the range and PMF of Y.
Homework Equations
Px(k) = p(1-p)^(k-1) for x=1,2,3...
3. My attempt at a solution
I set up the PMF for Px
Px(k) = 1/3(2/3)^(k-1) for k = 1,2,3,...
However I don't know how to convert this to Y