Question

x A probability density function of a random variable is given by f(x) = @ ż on the interval [4, 8]. Find the expected value, the variance, and the standard deviation. The expected value is u (Round to two decimal places as needed.)

Answer 1

# Given that! 4. 4 Jc 3 143 x2 42 8x3 272 Ox3 ={(64 - 64 시 fro= uc se Ye [4,8) u= E(X) = 5 x fcridx = 5°x(*++)dx = szujax Jo - Elementen -44)- 104)-646 - 4)] = {(21133–16) -(2-67-4)] = [ 5-33 +1:33] 16.66 EXPJ= Gºs?fon)dx= jºr(3-1)dx = situs *) dx ])-(4-11 = ((128–05:33)-(8-10.67)] = (42267 +2.67) = 145.34 V(X) = ECKP)-[ELM172 = 45.34-44:36* - 0.98 Standard deviation (o)= Jucx 10.98 0.90945 20.99 4 = x4 x 3 @x4 2x3 {6.033 44 (6.66) = 44-36 2 please give up rate if it is helpful to you.