Question

f(x) = { 1 x (3-X) it osx=2 Co otherwise

Let X be a random variable with probability density function

a) Find the mean of X

b) Find the standard deviation of X round to four decimal places.

c) Let G = X²  Find the probability density function f_G of G

Show work for each part plz

Answer 1

= f(x) = { / 0x (3-X) y OC XE2 0 میشلاق ) Mean of x = E(X) = Sx. f G ) di 2 x (3-x) da 194-* de (1) = [8-4] - *** - 2 Standard deviation of x ie ox = vv(x) Norway VCX) - EW*)-(EV)] .: E(X²) = 3 x². fte de Where v(x) = Kariame of x non 11 30² 3 x (3-x) dhe lo Dig to [18 22 - ** de 2

3 cq. 92 2 * [ 1-6 ] 1 = 20 [ 12 - 32 ] ( 60-7°) - Now. V(x) = E(X2) - [Ex] = -1 25 43 ) [from (i) fci)] Standard deviation of x = 0x = Vu (x) 3 G = X2 then f(n) ff, 0 <.X242 then fo) = f(x) = ²X2 (3-X2) G X2 t [0, 2] fo) = f(x2) = 0