Chapter 4: Q160S (page 281)

Given that xis a poisson random variable, compute $p (x)$ for each of the following cases:
a. $λ = 2, x = 3$
b. $λ = 1, x = 4$
c. $λ = 0.5, x = 2$

Short Answer

Expert verified

a. The probability distribution $p (x)$ is $\frac{4}{3} e^{- 2}$ .

b. The probability distribution $p (x)$ is $\frac{1}{24} e^{- 1}$ .

c. The probability distribution $p (x)$ is $0.125 \times e^{- 0.5}$ .

Step by step solution

Given information

X is a Poisson random variable.

Compute the probability distribution p(x) when λ=2,x=3

For a Poisson random variable, the probability distribution

$p (x) = \frac{λ^{x} e^{- λ}}{x!} : x = 0, 1, 2, . . .$

Here, $λ = 2, x = 3$

$p (x) = \frac{λ^{x} e^{- λ}}{x!} = \frac{2^{3} e^{- 2}}{3!} = \frac{8 \times e^{- 2}}{6} = \frac{4}{3} e^{- 2}$

Hence, the probability distribution $p (x)$ is $\frac{4}{3} e^{- 2}$ .

Compute the probability distribution p(x) when λ=1,x=4

Here, $λ = 1, x = 4$

$p (x) = \frac{λ^{x} e^{- λ}}{x!} = \frac{1^{4} e^{- 1}}{4!} = \frac{1}{24} e^{- 1}$

Hence, the probability distribution $p (x)$ is $\frac{1}{24} e^{- 1}$ .

Compute the probability distribution p(x) when λ=0.5,x=2

Here, $λ = 0.5, x = 2$

$p (x) = \frac{λ^{x} e^{- λ}}{x!} = \frac{{(0.5)}^{2} e^{- 0.5}}{2!} = 0.125 \times e^{- 0.5}$

Hence, the probability distribution $p (x)$ is $0.125 \times e^{- 0.5}$ .

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Given that xis a poisson random variable, compute $p (x)$ for each of the following cases:
a. $λ = 2, x = 3$
b. $λ = 1, x = 4$
c. $λ = 0.5, x = 2$

Short Answer

Step by step solution

Given information

Compute the probability distribution p(x) when λ=2,x=3

Compute the probability distribution p(x) when λ=1,x=4

Compute the probability distribution p(x) when λ=0.5,x=2

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Given that xis a poisson random variable, computep(x)for each of the following cases:a.λ=2,x=3b.λ=1,x=4c.λ=0.5,x=2

Short Answer

Step by step solution

Given information

Compute the probability distribution p(x) when λ=2,x=3

Compute the probability distribution p(x) when λ=1,x=4

Compute the probability distribution p(x) when λ=0.5,x=2

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Probability and Statistics

Geometry

Study anywhere. Anytime. Across all devices.

Given that xis a poisson random variable, compute $p (x)$ for each of the following cases:
a. $λ = 2, x = 3$
b. $λ = 1, x = 4$
c. $λ = 0.5, x = 2$