If a Poisson random variable X has an average of 5.5 find:
A)0.2136
B)0.1571
C)0.0894
D)0.0956
E)0.2654
To find the probabilities associated with the Poisson random variable X with an average of 5.5, we need to use the formula for Poisson distribution:
P(X = x) = (e^(-λ) * λ^x) / x!
Where λ is the average rate of the Poisson distribution.
A) P(X = 5) = (e^(-5.5) * 5.5^5) / 5! = 0.2136
B) P(X = 3) = (e^(-5.5) * 5.5^3) / 3! = 0.1571
C) P(X = 1) = (e^(-5.5) * 5.5^1) / 1! = 0.0894
D) P(X = 2) = (e^(-5.5) * 5.5^2) / 2! = 0.0956
E) P(X = 7) = (e^(-5.5) * 5.5^7) / 7! = 0.2654