QUESTION 10 5 points A Past Exam Question A Poisson distrib

QUESTION 10 (5 points) - A Past Exam Question A Poisson distribution has = 4.5 with the following probability distribution: 4 0 2 0.01111 0.049990.11248 0.16872 0.18981 0.17083 6 7 9 10 Px) 0.12812 0.08236 0633 0.02316 0.01042 0.00667 (a)[2] Find P(2 s x

Solution

(a) P(2<=x<8) = P(x=2) +P(x=3) +P(x=4) +P(x=5) +P(x=6) + P(x=7)

= 0.11248+0/16872+0.18981+0.17083+0.12812+0.09236

= 0.85232

(b) EF(x=0) = 0.01111 x 200 = 2.22 ~ 2

EF(x=1) = 0.04999 x 200 = 9.998 ~ 10

EF(x=2) = 0.11248 x 200 = 22.496 ~ 22

EF(x<=2) = P(x<=2) x 200 = [P(x=0) +P(x=1) +P(x=2)] x 200

= (0.01111+0.04999+0.11248) x 200

= 34.716 ~ 34