Consider a Poisson random variable with-6.5. Use the Poisson formula to calculat

Question

Consider a Poisson random variable with-6.5. Use the Poisson formula to calculate the following probabilities.(Round your answers to six decimal places.) (a) Px0) (b) Pix-1)- (c) Px 2) (d) P(x S 2)= -13 points MandStatt4 5.E.042 My Nenes Aak Your Toache or a binomial probability distribution with n 25 and 0.05 Round your ans ers to three To illustrate how ell the Poisson pro ability distribution approximates the binomial probability distribution, calculate the Posson approximate values forp 0 and p 1 decimal places.) p(o) Compare the answers with the exact values obtained from Table 1 in Appendix . They are opposites of each other. They are very close They are equal. Need Help? Tak to Tutor

Explanation / Answer

1) P(X = k) = (ke-)/k!

a) P(X = 0) = (0.50e-0.5/0! = 0.606531

b) P(X = 1) = (0.51e-0.5/1! = 0.303265

c) P(X = 2) = (0.52e-0.5/2! = 0.075816

d) P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.985612

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