Question

Assume a Poisson distribution. a. If lambda=2.5​, find ​P(X=5​). b. If lambda=8.0​, find ​P(X=10​). c. If lambda=0.5​, find ​P(X=0​). d. If lambda=3.7​, find ​P(X=4​). ROUND TO FOUR DECIMAL PLACES AS NEEDED

Answer 1

Solution :

Given that ,

mean = = = 2.5

Using Poisson probability formula,

P(X = x) = (e^- * ^x ) / x!

a)

P(X = 5) = (e^-2.5 * 2.5⁵⁾ / 5!

= 0.0668

Probability = 0.0668

b)

mean = = = 8

P(X = 10) = (e^-8 * 8¹⁰⁾ / 10!

= 0.0993

Probability = 0.0993

c

mean = = = 0.5

P(X = 0) = (e^-0.5 * 0.5⁰⁾ / 0!

= 0.6065

Probability = 0.6065

d)

mean = = = 3.7

P(X = 4) = (e^-3.7 * 3.7⁴⁾ / 4!

= 0.1931

Probability = 0.1931