Assingment C (2015)

A) For p=0.05, so q=0.95,

1. Binomial Distribution:

X B (n , p )

P(X=r) = C r0.05r×0.95n−r

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n

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N x 0 1 2 3 4 55 P(X=x) 0.77378 0.20363 0.021434 0.0011281 2.9688x10-5 3.125x10-7

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2. Poisson Distribution:

XP (np ) , λ=np= 5 x 0.05=0.25

P(X=r) = e−λ× λr

r !,

n r 0 1 2 3 4 55 P(X=r) 0.77880 0.19470 0.024338 2.0281x10-3 1.26758x10-4 6.3379x10-6

3. Normal Distribution:

X N (μ ,σ2 ) , μ=np=0.25 , σ2=npq=0.2375

Z=x−μσ,σ=√0.2375 ,P (X=r )=P (r−0.5<x<r+0.5)

n r 0 1 2 3 4 55 P(X=r) 0.63411 0.29882 5.1577

x10-51.9496x10-6

1.2960x10-11

1.3995x10-18

B) For p=0.1 , so q=0.9,

1. Binomial Distribution:

N x 0 1 2 3 4 55 P(X=x) 0.59049 0.32805 0.07290 8.1x10-3 4.5x10-4 1x10-5

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2. Poisson Distribution:

N r 0 1 2 3 4 55 P(X=r) 0.60653 0.30327 0.075816 0.012636 1.5795x10-3 1.57951

x10-4

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3. Normal Distribution:

N r 0 1 2 3 4 55 P(X=r) 0.43198 0.43198 0.066584 1.4307

x10-33.8744x10-6 1.2437x10-9

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C) For p=0.5, so q=0.5,

1. Binomial Distribution:

N x 0 1 2 3 4 55 P(X=x) 0.03125 0.15625 0.3125 0.3125 0.15625 0.0312510

2. Poisson Distribution:

N r 0 1 2 3 4 55 P(X=r) 0.082085 0.20521 0.25652 0.21376 0.13360 0.06680110

3. Normal Distribution:

N r 0 1 2 3 4 55 P(X=r) 0.033174 0.14873 0.31445 0.31445 0.14873 0.03317410