Question

Let A be a continuous random variable with probability density function

fa(a) = -a? 9 0<A<3

Random variable D is given by

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(a) What is the probability density function of D? specify the domain of D.

Answer is $f_{D}(d) = \frac{(D-1)^{2}}{243} \ \ \ \ \ \ \ \ \ \ if \ \ 1\leq D\leq 10$

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(b) Find E(D) and Var(D).

$Answer \ is \ E(D) = \frac{31}{4}, Var(D) = \frac{243}{80}$

Answer 1

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**@ 7.] 3 2 LxT (D-1) 27 g 2 Com fo (d) (D-1) 243 Now sine OLACI oC BALI LCBAt Clo 12 DE LO So pdf of D will im fold) (6-1) 2 iCollo 29.3 10 Now (0) ² (820 Di fold) do 10 is 2 Di (D-1) 243 db

2 (0-1) do 293 ut D-lat :-) Ott! =) do it at t=1tzo D210) Z Ittlit 293 Lot 474 193 4 t. +3 243 4 3 2:1 با 293 4- to 3 ㅗ 293 Х 33 (+) 1 x 3 + 1) 4 2749 le 4

-) E(D)= 31 Now E (62) = 102 D (P-1) 2 do. 243 ut D-1-4 ) Datti do=dt at D=1 = t-o D10 - ty 9 243 293 > E. (0²) = f (t+1?xt it so (+²+1 +24) t² at S: (+4+4? +243 Jelt 7+1+2**) 26 [1 + 2 + 1 st 203 293 < 3 a ㅛ 243 x9 92. + ģt 2 5 2

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