Question

You must show ALL (including u and du) steps to find the moment generating function. The integral ſex. f(x)dx where f(x) has the variable x (in our case it is also the function e*) leads to easy integration as long as u and du are properly defined. As you know from class lecture and book readings, a MGF has only the variablet, no x. After reviewing your materials, knowing that the function is continuous, find: a) the MGF for f(x) = where is a number and t < (this fact will lead to a 10 minus 1) when plugging the limits of integration in the final step, thus preventing the integral from diverging. b) Based on your finding above (you found o(t), take the first derivative relative to t, then sett to zero. c) Based on b) above, take the second derivative relative to t, then sett to zero. d) based on all of the above, and knowing that E(X)-[E(X)] = variance then find the variance and the standard deviation

Answer 1

Aust Given that let & is Raudan alariable and fCalebe , x>0 . (a). Mor of visi $ CH) = Cety) = rett foe) dx -t). = IC è l / 3 ta BL Cht) tot BE [8(t) = (1-P) 161 4 13 Scanned with CamScanner

(b) o'rt) - (1-2) fle) - BCI-P+74) - (C). Øl (H), c d d (€) E B 2. (l=Bhi? la molla 2B7(HBT? p"CHI. 28 (1-P)), e(x) = g (1) , (d). Varcx) = EC22) - (ECXIT? Cover 28- B = BP Var (x) = ß² & standard deviation = Jual ) CS CamScanne Standard deviation (x)=B), Scanned with

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