Problem 3. (10 points) Suppose that we have a random input and a random system. The input X is modeled as an exponential

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Problem 3 10 Points Suppose That We Have A Random Input And A Random System The Input X Is Modeled As An Exponential 1 (59.68 KiB) Viewed 20 times

Problem 3.
suppose that we have a random input and a random system.
The input X is modeled as an exponential random variable with
pdf
f_X (x)=λe^(-λx), x≥0, where λ >0 is fixed.
The output Y of the random system given the input {X=x} is
modeled by the Poisson law
Pr⁡(Y=y│X=x)=e^(-x) x^y/y!,for y=0,1,…
Find the pmf of Y.
Problem 3. (10 points) Suppose that we have a random input and a random system. The input X is modeled as an exponential random variable with pdf –λα fx (x) = le = x > 0, = where > 0 is fixed. The output Y of the random system given the input {X = x} is modeled by the Poisson law Pr(Y = y|X = x) = 2 .2.3 = = =é for y = 0, 1, ... y!' Find the pmf of Y.