Question

Let X be the number of material anomalies occurring in a particular region of an aircraft gas-turbine disk. A researcher proposes a Poisson distribution for X. Suppose that i = 6. The Poisson probability mass function is: 1 - 1 P(X = r) = r! for x = 0,1,2,... Use the pmf to calculate probabilities. Verify these values in R using dpois(x,lambda). Compute the following probabilities: (Round your answers to three decimal places.) (a) P(X = 5) = (b) PCX 55) = (C) P(X<5) = (d) P(X> 5) = (e) P(4SXS 8) =

Answer 1

a)

probability =

P(X=5)=

{e-λ*λx/x!}=

0.161

b)

probability =

P(X<=5)=

∑x=0x   {e-λ*λx/x!}=

0.446

c)

probability =

P(X<=4)=

∑x=0x   {e-λ*λx/x!}=

0.285

d)

probability =

P(X>=6)=

1-P(X<=5)=

1-∑x=0x-1   {e-λ*λx/x!}=

0.554

e)

probability =

P(4<=X<=8)=

∑x=x1x2   {e-λ*λx/x!}=

0.696