Whether the statement is true or false.

kuCAu 2021-02-06 Answered
Whether the statement is true or false.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Corben Pittman
Answered 2021-02-07 Author has 83 answers

We have to determine the sum of two independent Poisson random variables has a Poisson distribution.
Let X and Y are two Poisson random variables with parameters λ1 and λ2.
Hence, the moment-generating functions are:
MX(t)=eλ1+λ1et
MY(t)=eλ2+λ2et
By theorem,
MX+Y(t)=Mx(t)My(t)
MX+Y(t)=eλ1+λ1eteλ2+λ2et
MX+Y(t)=e(λ1+λ2)e(λ2+λ2)et)
Hence, the moment-generating function of X+Y is a moment:
generating function of Poisson distribution with parameter λ1+λ2.
That means X+Yis alsofollows a Poisson distribution with parameter λ1+λ2.
Therefore, the statement sum of two independent Poisson random variables has a Poisson distribution is true.

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-03-18

A population of values has a normal distribution with μ=133.5 and σ=5.2. You intend to draw a random sample of size n=230.
Find the probability that a single randomly selected value is between 133.6 and 134.1.
P(133.6<X<134.1)=?
Write your answers as numbers accurate to 4 decimal places.

asked 2021-02-21

We wish to estimate what percent of adult residents in a certain county are parents. Out of 600 adult residents sampled, 192 had kids. Based on this, plot a 99% confidence interval for the proportion of adult residents who are parents in a given county.
Express your answer in the form of three inequalities. Give your answers in decimal fractions up to three places <p< Express the same answer using a point estimate and a margin of error. Give your answers as decimals, to three places.
p=±

asked 2021-02-09
If X and Y are random variables and c is any constant, show that E(c)=c.
asked 2021-02-12
Discrete or Continuous? Identify the following as discrete or continuous random variables:
a. Total number of points scored in a football game
b. Shelf life of a particular drug
c. Height of the oceans
asked 2021-08-05

Five people have a genetic disease and one child each. The random variable x is the number of children among the five who inherit the​ disease.
a)Find the mean.
b)Find the standard deviation.
x012345P(x)0.0270.1620.3110.3110.1620.027

asked 2021-03-02

CNNBC recently reported that the mean annual cost of auto insurance is 954 dollars. Assume the standard deviation is 271 dollars. You take a simple random sample of 96 auto insurance policies.
Find the probability that a single randomly selected value is less than 969 dollars.
P(x<969)=P(x<969)=?

Write your answers as numbers accurate to 4 decimal places.

asked 2021-02-09
If X and Y are random variables and c is any constant, show that E(X+Y)=E(X)+E(Y).