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Probability Calculation with Independent Random Variables
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Probability Calculation with Independent Random Variables

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Questions and Answers

Define a new random variable Z as Z = min(X, Y). What is the CDF of Z?

FX(z) + FY(z) - FX(z)FY(z)

If X and Y are two independent random variables with PMFs given as fX(k) = fY(k) = 1/6 for k = 1, 2, 3, 4, 5, 6, find the value of fZ(3) where Z = X - Y.

1/12

If X follows Geometric(p) distribution and Y follows Geometric(p) distribution, and Z = X + Y, determine the values of p for which P(Z = 26) > P(Z = 25).

p < 1/25

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