Question

O A Gamma random variable x with parameters xson Bo has the following moment generating function: M(t) = (1 - 45 for taß (9 pts) . Use the reg.f. Mit given above E(X4), (where X is a Canan c.v.) to calculate (9 pts) [ Use the mg.f. Mit given above to calculate the standard deviation of a Gamma rov. X. (9 pts) © The skewness of a r.V. X, with mear=u& std. dev. = T, is given by : skewness (X) = g(x-x)" ] Use the mag.f. McEl given above to calculate the skewness of a Gamma r... You can use that : (a-b)² = 23-32²6 +3ab²-63

Answer 1

is a Gamma random variable. that has Mx (t) 7 x as 3 Mx (t) = (1-tja Malt) = E(X2) TE=0 - move, a Mall) -411-+) {o } - elefantis (1-2 dt2 xCat) o po? :: E(X2) = (x+1) 0=8D = JvLX) - JE 6x2) - 8°(X) According to the problen done above

ت : 85 مياء = 4 E) - 2 . ( 1t=8 1 - 0 و کمان کا SD SD = (دا : =E(x2) - E1 (x) 0 -2 IT وه NOW يساعده ع = ( مت

F{X_M)]= [x®= 65°W + 3xque -. Mos] = E[x]- 3u E(X2) + Blee(x) – juee = alet) lutz) Gualatt) + s permet - us $3

Mean= U- => SK = - The Cast)lar 2) – Balatt) + 3x2_x? ta [ 2448x +*+2 +846: t.exe]