Use the poisson formula to find the probability of the value given for the random variable x.
1. M = 2, x = 3 2. M = 4, x = 1 3. M = 0.845, x = 2 4. M = 0.250, x = 2
Solution:
1)Given that ,
mean = M = 2
Using Poisson probability formula,
P(X = x) = (e^{-M} * M^{x} ) / x!
P(X = 3) = (e^{-2}* 2 ^{3)} / 3! = 0.18045
2) Given that ,
mean = M = 4
Using Poisson probability formula,
P(X = x) = (e^{-M} * M^{x} ) / x!
P(X = 1) = (e^{-4}* 4^{1}^{)} / 1! = 0.07326
3)Given that ,
mean = M = 0.845
Using Poisson probability formula,
P(X = x) = (e^{-M} * M^{x} ) / x!
P(X = 2) = (e^{-0.845}* 0.845^{2}^{)} / 2! = 0.15336
4) Given that ,
mean = M = 0.250
Using Poisson probability formula,
P(X = x) = (e^{-M} * M^{x} ) / x!
P(X = 2) = (e^{-0.250}* 0.250^{2}^{)} / 2! = 0.02434
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