Answer to Question #304187 in Statistics and Probability for ekamanga

Question #304187

Suppose the time spent by a randomly selected student at a campus computer lab has a gamma distribution with mean 20 minutes and variance 80 minutes.


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Expert's answer
2022-03-01T16:00:40-0500

a. What are the values of αα and ββ


μ=αβ=20\mu =\alpha \beta=20

σ2=αβ2=80\sigma^2=\alpha \beta^2=80

β=8020=4\beta=\dfrac{80}{20}=4

α=204=5\alpha=\dfrac{20}{4}=5

b. What is the probability that a student uses the terminal for at most 24 min?


P(X24)=F(24;α,β)=F(24/β;α)P(X\le 24)=F(24;\alpha, \beta)=F(24/\beta;\alpha)

=F(24/4;5)=F(6;5)=0.7149=F(24/4;5)=F(6;5)=0.7149

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