For each of the following situations: i. describe how you could compute the prob

Question

For each of the following situations: i. describe how you could compute the probability with appropriate pmfs or pdfs (note, you do not actually need to do this, just describe how it could be done), and ii. use R to compute the probability and report the probability and the R code you used in your answer. Be sure to label your answers clearly (i.e., with a-g and i-iii). a. X_a is normally distributed with mu = 12 and sigma^2 = 4. Compute P(X_a greaterthanorequalto 14). b. X_b has a gamma distribution with mean 4 and standard deviation 8. Compute P(4 lessthanorequalto X_b

Explanation / Answer

ii-a) In ND, P(X>14) = 0.158655

R-code:

> 1-pnorm(14,12,2)
[1] 0.1586553

ii-b) In Gamma distribution

Mean = 4 and variance = 64

as = 4 and as^2 = 64

4*s =64 Therefore, s=16, a = 1/4

P(4<X<10) =

R-code:

> pgamma(10,1/4,1/16) - pgamma(4,1/4,1/16)
[1] 0.1332078

ii - c)

> ppois(1,lambda=0.7)
[1] 0.844195

ii-d)

> 1-pchisq(4,5)
[1] 0.549416

ii-e)

> dnbinom(5,5,0.5)
[1] 0.1230469

ii-f)

> plnorm(10,2,1)
[1] 0.618897

ii-g)

> pweibull(7,2,7)
[1] 0.6321206

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