Given that x has a Poisson distribution with μ = 0.8, what is the probability that x = 1?
P(1) ≈ (Round to four decimal places as needed.)
Answer (2)
The probability that a Poisson random variable x equals 1 with a mean μ = 0.8 is calculated using the Poisson formula, resulting in approximately 0.3594 .
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To find the probability of a Poisson random variable with a given mean μ , we use the Poisson probability formula:
P ( x = k ) = k ! e − μ ⋅ μ k
In this case, the mean μ = 0.8 and k = 1 . Let's substitute these values into the formula:
P ( x = 1 ) = 1 ! e − 0.8 ⋅ 0. 8 1
Calculate each component step-by-step:
Calculate e − 0.8 :
Using a calculator:
e − 0.8 ≈ 0.4493
Calculate 0. 8 1 :
0. 8 1 = 0.8
Calculate 1 ! :
1 ! = 1
Putting it all together:
P ( x = 1 ) = 1 0.4493 ⋅ 0.8 = 0.3594
So, the probability that x = 1 is approximately 0.3594. Make sure to round the final answer to four decimal places as needed.
