Question

Suppose *X* has a Poisson distribution with a mean of
1.5. Determine the following probabilities. Round your answers to
four decimal places (e.g. 98.7654).

**(a)***P*(*X* = 1)

**(b)***P*(*X* ≤ 3)

**(c)***P*(*X* = 7)

**(d)***P*(*X* = 2)

Answer #1

Solution :

Given that ,

mean = = 1.5

Using poisson probability formula,

P(X = x) = (e^{-}
*
^{x} ) / x!

a) P(X = 1)

P(X = 1) = (e^{-1.5} * 1.5^{1} / 1! )

P(X = 1) = 0.3347

Probability = 0.3347

b) P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= (e^{-1.5} * 1.5^{0} / 0! ) + (e^{-1.5}
* 1.51/ 1! ) +
(e^{-1.5} * 1.5^{2} / 2! ) + (e^{-1.5} *
1.5^{3} / 3! )

= 0.2231 + 0.3347 + 0.251 + 0.1255

= 0.9344

Probability = 0.9344

c) P(X = 7) = (e^{-1.5} * 1.5^{7} /
7! )

= 0.00000005

Probability = 0.0000005

d) P(X = 2) = (e^{-1.5} * 1.5^{2} /
2! )

= 0.2510

Probability = 0.2510

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