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In a Poisson distribution µ = 4.a. What is the probability
Chapter 6, Problem 26E(choose chapter or problem)
QUESTION:
In a Poisson distribution \(\mu=4\).
a. What is the probability that x = 2?
b. What is the probability that \(x \leq 2\)?
c. What is the probability that x > 2?
Questions & Answers
QUESTION:
In a Poisson distribution \(\mu=4\).
a. What is the probability that x = 2?
b. What is the probability that \(x \leq 2\)?
c. What is the probability that x > 2?
ANSWER:Step 1 of 3
(a) We are asked to find the probability that x = 0
Given that Poisson distribution with mean \(\mu=4\)
The probability mass function (PMF) of Poisson distribution is
\(\begin{array}{l}
P(X=x)=\frac{e^{-\mu} \mu^{x}}{x !}\\
\begin{aligned}
P(X & =2)=\frac{e^{-4}(4)^{2}}{2 !} \\
& =0.1465
\end{aligned}
\end{array}\)
Hence the probability of x = 0 is 0.1465