Lg;- : ( Jo 'J i XLZMD' l-(Z:O,IOZH Il X3(3KA Li) ': nea/Ii", " La 4 I ' O 2 Lu W52 - (DL-Bu" / a Let X have the exponential pdf, f(x) = B'"exp(-x/B),m "- M- , , a) Find the moment generating function l m -- . (z' r , ' ' :x-(e"- to")..-,>'2; {ix/N, N if; 'Jl EV : J ' v/x '.-' , " U "'7" . II, " "Cl 1, 1 l ! ' ' xi; - ? J / X j / ' 7 fl) I "'o v '7 O ' fl.- f XLOJ- /P X / fl" " i. 'I i " -' F to" , 2 ' '- / ' r":7 2-7 ,. - " 0 OCR? v '* 'x r .. ' p r fi'fifke'ww :. .. i H ,. ' 7- . 2'"-" b' ' d ' e'" ' ' i : t - l or J '1' . ' ' " LL ,-, x-l LA, " L/ '4 ' j" 9 J ' lg- on, x' " . i l . 0 0 L, : " V " iv x , x -: s 'z CL; ' JLx Ax3 . l bi) Prove that the mean of the exponential distribution is B using the moment generating function