Question: Let X be a Poisson random variable with = 2 and Y be a Poisson random variable with = 4. Assume X and

Let X be a Poisson random variable with λ = 2 and Y be a Poisson random variable with λ = 4. Assume X and Y are independent. Find the following probabilities.

(a) P(X<4, Y<4)

(b) P(X≥ 2, Y<4)

(c) P(2≤X<4, Y≥3)

(d) P(X<5, 1≤ Y ≤4)

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