Given that X is a random variable having a Poisson(A) distribution, compute the following: (a) P(X- 2) when A 5 P(X 2) (b) P(X < 8) when A 1 P(X<8) = (c) P(X> 1) when X 5.5 P(X> 1) = (d) P(X< 5) when A 4 P(X<5)-

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A: given data, binomial distribution n=10p=0.5x= no of successp(X=x) = Cx n * px *qn-x

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Q: a) P(X=5) when λ=2.5 P(X=5)= (b) P(X≤5) when λ=4 P(X≤5)= (c) P(X>3) when λ=0.5 P(X>3)=

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A: i) Since, -2&lt;1.8&lt;2 , so F(1.8) follows 0.25x+0.5 P(X &lt; 1.8)=F(1.8)=0.25(1.8)+0.5=0.95

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Q: If X is a Poisson random variable with a rate of 5. Then, Calculate the probability P( X < 2)?

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Q: Then find E[X], E[X2], E[2X+5], E[(X+1)²].

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Q: Given that X is a random variable having a Poisson(A) distribution, compute the following: (a) P(X=…

A: We know that, The probability mass function is,  P(X=x) = (e-λ×λx)/x!  Where,  λ &gt; 0  x = 0, 1,…

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A: The provided information are: Meanμ=0.75Varianceσ2=0.7125

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Q: (a) P(x≤ a) = 0.42 a = (b) P(x a) = 0.32 a =

A: a) Suppose the random variable x defines the Uniform probability distribution from 0 to 5.

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A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are…