Solved: Suppose that X has a Poisson distribution with a

Chapter 3, Problem 158E

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QUESTION:

Suppose that X has a Poisson distribution with a mean of 0.4. Determine the following probabilities:

(a) \(P(X=0)\)                 (b) \(P(X \leq 2)\)

(c) \(P(X=4)\)                 (d) \(P(X=8)\)\)

Equation transcription:

Text transcription:

P(X=0)

P(X \leq 2)

P(X=4P(X=8))

P(X=8)

Questions & Answers

QUESTION:

Suppose that X has a Poisson distribution with a mean of 0.4. Determine the following probabilities:

(a) \(P(X=0)\)                 (b) \(P(X \leq 2)\)

(c) \(P(X=4)\)                 (d) \(P(X=8)\)\)

Equation transcription:

Text transcription:

P(X=0)

P(X \leq 2)

P(X=4P(X=8))

P(X=8)

ANSWER:

Solution 158E

Step1 of 5:

Let us consider a random variable X it follows poisson distribution with parameter

Here our goal is:

a). We need to find

b). We need to find

c). We need to find

d). We need to find


Step2 of 5:

a).

Suppose that a random variable X follows Poisson distribution with parameters ‘

Then, the probability mass function of poisson distribution is given by:

                  x = 0,1,2,...

Now,

                   

                     

Therefore, P(X = 0) = 0.6703.


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