Assume that the variable X is distributed as a Poisson with λ = 5.7. Calculate the following probabilities.
a. Pr( X = 1 )
b. Pr( X < 1 )
c. Pr( X > 1 )
d. Pr( X ≤ 1 )
Solution :
Given that ,
mean = = 5.7
Using poisson probability formula,
P(X = x) = (e- * x ) / x!
a)
P(X = 1) = (e-4.3 * 5.71) / 1! = 0.0191
Probability = 0.0191
b)
P(X < 1) = P(X = 0) = (e-4.3 * 5.70) / 0! = 0.0033
Probability = 0.0033
c)
P(X > 1) = 1 - P(X 1) = 1 - [P(X = 0) + P(X = 1) ]
= 1 - 0.091 - 0.0033
= 0.9776
Probability = 0.9776
d )
P(X 1) = P(X = 0) + P(X = 1) ] = 0.091 + 0.0033 = 0.0224
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