Q160S Given that x聽is a poisson rando... [FREE SOLUTION]

91影视

Statistics For Business And Economics

James T. McClave, P. George Benson, Terry Sincich

$Math Studyset 91影视 Explanations$ Math

13th Edition 路 888 pages

ISBN: 9780134506593

Chapter 4: Q160S (page 281)

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

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 $0.125 脳 e^{- 0.5}$ .

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

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

Here, $位 = 2, x = 3$

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

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

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

Here, $位 = 1, x = 4$

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

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, $位 = 0.5, x = 2$

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

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

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91影视

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

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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91影视

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

Statistics

Probability and Statistics

Applied Mathematics

Pure Maths

Logic and Functions

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

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