poissexamp

poissexamp - More Examples, Poisson Distribution Example 1...

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More Examples, Poisson Distribution Example 1 Suppose that the number X of tornados observed in a particular region during a one-year period has a Poisson distribution with ¸ = 8 . a. Compute P ( X · 5) , P (6 · X · 9) , and P (10 · X ) . Solution The desired probabilities are: P ( X · 5) = 5 X x =0 exp( ¡ 8)8 x x ! = 0 : 1912 P (6 · X · 9) = 9 X x =6 exp( ¡ 8)8 x x ! = 0 : 5254 P (10 · X ) = 1 X x =10 exp( ¡ 8)8 x x ! = 0 : 2834 : b. How many tornados can be expected to be observed during the one-year period and what is the standard deviation of the number of observed tornados? Solution E ( X ) = ¸ = 8 , ¾ X = p ¸ = p 8 = 2 : 8284 : Example 2 Consider writing onto a computer disk and then sending it through a certi…er that counts the number of missing pulses. Suppose this number X has a Poisson distribution with ¸ = 0 : 2 . a. What is the probability that a disk has exactly one missing pulse? Solution P ( X = 1) = exp( ¡ 0 : 2)0 : 2 1 1! = 0

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poissexamp - More Examples, Poisson Distribution Example 1...

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