Suppose X has a Poisson distribution with a mean of .4. How would i find the probability when X=0, X=4, X≤2, and when X=8?

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Terry Ray · Accepted Answer

P(X=0),λ=0.4  P(X=0)=e−λλkk!=e−0.4(0.4)00!=(0.670320)×(1)1=0.670320  Use excel function POISSON.DIST (X, mean, cumulative) to calculate PX(0):  POISSON.DIST (0, 0.4, FALSE) =0.670 320 046 036  P(X=0)=0.6703  P(X=4),λ=0.4  P(X=4)=e−λλkk!=e−0.4(0.4)44!=(0.670320)×(0.0256)24=0.000715  Use excel function POISSON.DIST (X, mean, cumulative) to calculate PX(4):  POISSON.DIST (4, 0.4, FALSE) =0.000 715 008 049 105  P(X=4)=0.0007  P(X≤2),λ=0.4  P(X≤2)=P(0≤X≤2)=P(X=0)+P(X=1)+P(X=2)  P(X=0)=e−λλ00!=e−0.4(0.4)00!=0.670320  P(X=1)=e−λλ11!=e−0.4(0.4)11!=0.268128  P(X=2)=e−λλ22!=e−0.4(0.4)22!=0.053626  Answer = 0.670320+0.268128+0.053626=0.992074  Use excel function POISSON.DIST (X, mean, cumulative) to calculate  P(X≤2)=FX(2): POISSON.DIST (2, 0.4, TRUE)=0.992073668133  P(X≤2)=0.9921  P(X=8),λ=0.4  P(X=8)=e−λλkk!=e−0.4(0.4)88!=(0.670320)×(0.000655)40320=0  Use excel function POISSON.DIST (X, mean, cumulative) to calculate

Suppose X has a Poisson distribution with a mean of

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