Poisson distribution

Question 1

What are the conditions for a Poisson distribution

Answer 1

The events occur singular
The events are independent of one another
The average rate of events is constant

Question 2

If a random variable X follows a Poisson distribution X~Po(λ) then what is P(X=x)

Answer 2

e^-λ.λ^x/x!

Question 3

If a random variable X follows a Poisson distribution X~Po(λ) then what is E(X)

Answer 3

λ

Question 4

If a random variable X follows a Poisson distribution X~Po(λ) then what is Var(X)

Answer 4

λ

Question 5

If a random variables X and Y follow Poisson distributions such that X~Po(λ) and Y~Po(μ) and Z = X+Y, how can Z be expressed as a distribution

Answer 5

Z~(λ+μ)