Get the solution to "Consider a Poisson distribution with μ=3. What is..."

idiopatia0f

Answered question

2022-01-16

Consider a Poisson distribution with

μ = 3

. What is

P (x \geq 2)

Archie Jones

Beginner2022-01-16Added 34 answers

Explanation:
The Poisson distribution is

P (x) = \frac{e^{- μ} μ^{x}}{x!}

μ = 3

3! = 3*2*1

P (x \geq 2) = 1 - P (1) - P (0)

P (1) = \frac{e^{- 3} \cdot 3^{1}}{1!} = \frac{3}{e^{3}}

P (0) = e^{- 3} = \frac{1}{e^{3}}

Therefore,

P (x \geq 2) = 1 - P (1) - P (0) = 1 - 0.0498 - 0.1494 = 0.8009

Explanation:
In a Poisson probability distribution, if mean value of success is

μ

,
the probability of getting x successes is given by

P (x) = \frac{e^{- μ} μ^{x}}{x!}

Now

P (x \geq 2)

means 1-P(x=0)-P(x=1)
Here

μ = 3

and

e^{- μ} = e^{- 3} = 0.049787

and hence, desired probability is

1 - \frac{e^{- 3} 3^{0}}{0!} - \frac{e^{- 3} 3^{1}}{1!}

= 1 - e^{- 3} \times (1 + 3)

= 1 - 0.049787 \times 4

=1-0.199148
=0.800852

peterpan7117i

Beginner2022-01-17Added 39 answers

Compute

P (X \geq 2)

The required probability is

P (X \geq 2) = 1 - P (X < 2)

=1-[P(X=0)+P(X=1)]
=1-[0.049787+0.149361] from statistical table
=0.8009
The required

P (X \geq 2) = 0.8009

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