Chapter 8: Poisson Distribution.

Question 1

What 4 things does X have to follow to use a Poisson Distribution?

Answer 1

• X has be be a whole number of events in a given period.
• The events must occur randomly and independently.
• The events must happen singly (one at a time).
• The events must happen at a constant rate.

Question 2

What do you write if the discrete random variable X follows a Poisson Distribution?

Answer 2

X ~ Po(λ)

Question 3

What does the mean equal for a poisson distribution?

Answer 3

λ (Poisson Parameter).

Question 4

What does the variance equal for a poisson distribution?

Answer 4

λ (Poisson Parameter).

Question 5

Are the mean and variance equal for a Poisson Distribution?

Answer 5

Yes, they both equal, λ (Poisson Parameter).

Question 6

How do you find the variance from the Standard Deviation?

Answer 6

Variance = (S.D)².

Question 7

What happens if the time period of a Poisson Distribution changes?

(e.g. 1 day to 1 week).

Answer 7

You have to multiply ‘λ’ by the difference. X ~ Po(nλ). Where ‘n’ is the scalar product.

X ~ Po(λ) would go to X ~ Po(7 x λ).

Question 8

What is the formula for if you add 2 different independent random variables?

X ~ Po(λ) and Y ~ Po(δ)

Answer 8

X ~ Po(λ) + Y ~ Po(δ)
–>
X + Y ~ Po(λ + δ).