Y is an exponential random variable with parameter 1 = 0.2. Given the event A = {Y < 2}, a. What is the conditional PDF, fy|a(y)? b. Find the conditional expected value E[Y|A]?

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Y is an exponential random variable with parameter 1 =
0.2. Given the event A = {Y < 2},
%3D
a. What is the conditional PDF, fy|A(y)?
b. Find the conditional expected value E[Y|A]?
Ans. A) fyja(y) = ÷ 5 (0 < y< 2); 0 otherwise B) E[T] = 0.9335
1 e-y/5
51-e-2/5
Transcribed Image Text:Y is an exponential random variable with parameter 1 = 0.2. Given the event A = {Y < 2}, %3D a. What is the conditional PDF, fy|A(y)? b. Find the conditional expected value E[Y|A]? Ans. A) fyja(y) = ÷ 5 (0 < y< 2); 0 otherwise B) E[T] = 0.9335 1 e-y/5 51-e-2/5
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