For the given values of the random variable X, fill in the corresponding probabilities

Short Answer

Expert verified
X=x
role="math" localid="1648582898375" P(X=x)
0
P(X=0)=e-8800!=0.00033
1
role="math" localid="1648582946177" P(X=1)=e-8811!=0.00268
2
P(X=2)=e-8822!=0.01073
3
role="math" localid="1648583006514" P(X=3)=e-8833!=0.02862
4
P(X=4)=e-8844!=0.05725

Step by step solution

01

:Given

Eighteen teens on average dies due to motor vehicle accident every day.
Formula used:
P(X=x)=e-λxx!

02

:Explanation of Solution

Interpretation:
Xis a arbitrary variable who represents the no. of teens who die because of motor vehicle injuries.Xcan take any value 0,1,2,3,4...According to the given situation, we can clearly say that Xfollows the Poisson Distribution with parameter mean (λ)is 8 per day and variance(λ) is also 8 per day. In Poisson distribution Variance is equals to mean.
Poisson distribution occurs when there is not definite no. of trials orn and occurrence of no. of events in a fixed time interval is fixed.
Probability mass function of Poisson distribution isP(X=x)=e-xxxxx! x=0,1,2,3,4,
We have used above mentioned probability mass function to get the probabilities

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