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標題:

poisson distribution

發問:

Let X~Po(5) and k be a non-negative integer. If P(X >= k ) >0.7, find the greatest value of k.

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P(X = 0) = e^(-5) = 0.006738 P(X = 1) = 5e^(-5) = 0.0337 P(X = 2) = 25e^(-5)/2 = 0.0842 P(X = 3) = 125e^(-5)/6 = 0.1404 P(X = 4) = 625e^(-5)/24 = 0.1755 P(X = 5) = 3125e^(-5)/120 = 0.1755 P(X = 6) = (5^6)e^(-5)/720 = 0.1462 P(X <= 3) = 0.265038 So, the greatest value of k is 4

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