Question #25064

Suppose that X has a Poisson distributions if P(X=1)=0.3 and P(X=2)=0.2, calculate P(X=0) and P(X=3).

Expert's answer

Poisson distributions:

P ( m, X) = m^X *Exp[-m]/X!

m - the expected value of X

P(X=1)= m*Exp[-m] = 0.3

P(X=2)= m^2*Exp[-2m]/2 = 0.2

For example, from the first equation:

m = 0.48

P(X=0) = Exp[-m]= 0.62

P(X=3) = m^3*Exp[-3m]/6 = P(X=1)*P(X=2)/3 = 0.2*0.3/3 = 0.02 &

P ( m, X) = m^X *Exp[-m]/X!

m - the expected value of X

P(X=1)= m*Exp[-m] = 0.3

P(X=2)= m^2*Exp[-2m]/2 = 0.2

For example, from the first equation:

m = 0.48

P(X=0) = Exp[-m]= 0.62

P(X=3) = m^3*Exp[-3m]/6 = P(X=1)*P(X=2)/3 = 0.2*0.3/3 = 0.02 &

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