Question

For this exercise, give exact answers as simplified fractions. Compute E (X) and Var (X) if X has probability density function given by ... c(1-26) if –1<<1 a) fx(r) = 10 otherwise Determine the value of cas part of your answer. c/ if b) fx(x) = > 5 10 otherwise Determine the value of cas part of your answer. Hint: The variance does not necessarily need to be finite.

Answer 1

(a) f(2)= c(1-26) if 12261 otheticise A8 x (x) is a P.D.F fx (x) dxal (1-x ) dx = 1 I (1-x6) dx=1 - с 7 to Ti- (-1) + (7 --

E(x) = (x f (x) dx s. 7(1-x) dx 8 - - (-12 + sy 20 E (x2) x2 f (x) da x² x 7 (126) da

. 2 - ابن آد م به Var (x) = E(x2)- €?(x) = -09

(6) fx (x ) = 5 or if x55 o otherweise As, x(x) is a P.D.F. I f (x) dx = 1 25 de 40 -Sun 1 2 -5 + 1 & co-5-4 - 4.54 a c=5.4 = 2500

Elx). 2.500 2570 x D 5 = 2500 = 2500 3 x 53 2500 375 = 6.6667 E(X2) - 1 2 2500 0x - 3 da - 2500 - 2500xo-2 2500 X - 2 2000 10050 - 7x25 50

Var (x) = E(X2) – E²x) = 50- (6.6667) - 50 – 44.44489 5.555