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a. Find thedistribution (mass function or cdf) of X + Y
b. CalculateP(X=1|X+Y=1) Suppose that X and Y are indicator random variables for the events
A and B, respectively; that is
Solution
distribution function of X+Y is P(X+Y=0) = (1-1_a)(1-1_b) ie neither of A & B
occur P(X+Y=1) = 1_a + 1_b - 1_a*1_b ie either A occurs or B occurs but not both. The both
occur case is subtracted as 1_a*1_b. P(X+Y=2) = 1_a*1_b. P is zero for all other values. b.
P(X=1|X+Y=1) = P( X=1 and X+Y=1) / P(X+Y=1) if X=1 and X+Y=1 implies Y=0. so required
probability is P(X=1 and Y=0) / P(X+Y=1) = [ 1_a (1 - 1_b) ]/ [ 1_a + 1_b - 1_a*1_b] 1_a is
indicator rv for A and 1_b is indicator rv for B.

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a. Find thedistribution (mass function or cdf) of X + Yb. Calculat.pdf

  • 1. a. Find thedistribution (mass function or cdf) of X + Y b. CalculateP(X=1|X+Y=1) Suppose that X and Y are indicator random variables for the events A and B, respectively; that is Solution distribution function of X+Y is P(X+Y=0) = (1-1_a)(1-1_b) ie neither of A & B occur P(X+Y=1) = 1_a + 1_b - 1_a*1_b ie either A occurs or B occurs but not both. The both occur case is subtracted as 1_a*1_b. P(X+Y=2) = 1_a*1_b. P is zero for all other values. b. P(X=1|X+Y=1) = P( X=1 and X+Y=1) / P(X+Y=1) if X=1 and X+Y=1 implies Y=0. so required probability is P(X=1 and Y=0) / P(X+Y=1) = [ 1_a (1 - 1_b) ]/ [ 1_a + 1_b - 1_a*1_b] 1_a is indicator rv for A and 1_b is indicator rv for B.