Question

11. Time spent on a computer denoted by X is gamma distributed with mean 20 min and variance 80 min. a) What are the values of a and B? b) Use R to find P(X < 24)? c) Use R to find P(20 < X< 40)?

Answer 1

11. a. Let X follows gamma distribution with scale parameter = 1/B. shape parameter = a then E(X) = mean = = 20, Var(X) = = 80 E(X) = 3 = 20/80 = 0.25 Var(x) = 3 = 20/80 = 0.25 then a = 203 = 20 * 0.25 = 5 6. P(X<24) = 0.7149 R code: round(pgamma(24, shape = 5, scale = 1/0.25), 4) c. P(20 < X < 40) = 0.4112 R code : round pgamma( 40, shape = 5, scale = 1/0.25) - pgamma(20, shape = 5, scale = 1/0.25), 4)

Answer 2

Better=4 Alpha =5