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..
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.
![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.](https://image.slidesharecdn.com/a-230324063445-99475ab9/85/a-Find-thedistribution-mass-function-or-cdf-of-X-Yb-Calculat-pdf-1-320.jpg)
