Question

i had to put two pictures becahse the whole question did not fit on my screen

The two parameter gamma distribution can be generated by introducing a third parameter y, ed a threshold or location parameters replace xin (.8). (4.7) 0 otherwise by X Y and 2 by x 2 y. This amounts to shifting the density curves in the figure below so that the begin their scent or descent at rather than 0. (alguna density Curves 12. SY 4 (very close to estimates in the cited article A study employs this distribution to model day food volume (10m). Suppose that values of the parameters are based on past data) a What are the mean value and standard deviation of X7 Round your answers to four decimal places) mean 10m standard deviation What's the probability that rood volumes between 100 and 150 Round your answer to three decimal places)

Answer 1

a)

mean μ =

αβ =12*8+44

140

standard deviation σ=β*√α=

27.7128

b)

from excel: P(100<X<153) =gammadist(153-44,12,8,true)-gammadist(100-44,12,8,true)=0.654

c)P(X>140+27.7128)=1-gammadist(140+27.7128-44,12,8,true)=0.156

d)

95th percentile =gammainv(0.95,12,8)+44=189.66