poisson stat

Question

The random variable X follows a Poisson process with the given value of

lambdaλ

and t. Assuming

lambdaλequals=0.130.13

and

tequals=1515​,

compute the following.

​(a)

​P(55​)

​(b)

​P(Xless than<55​)

​(c)

​P(Xgreater than or equals≥55​)

​(d)

​P(33less than or equals≤Xless than or equals≤77​)

​(e) mu Subscript Upper X Baseline and sigma Subscript Upper X

Answer 1

Po(X)=(λt)ᵡe^-(λt)/X! µ=σ²=λt=0.13×15=1.95.

a) Po(X=5)=1.95⁵e⁻¹⋅⁹⁵/5!=0.03343.

b) Po(<5)=Po(0)+Po(1)+Po(2)+Po(3)+Po(4)=

0.14227+0.27743+0.27050+0.17582+0.08571=0.95175 approx. (95.18%)

c) Po(≥5)=1-0.95175=0.04825 approx. (4.83%)

d) Po(3≤X≤7)=Po(3)+Po(4)+Po(5)+Po(6)+Po(7)=

0.17582+0.08571+0.03343+0.01086+0.00303=0.30886 approx. (30.89%)

e) µ=1.95, σ=√1.95=1.40 approx.