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1. find the expected value of the random variable y whose probability density is given by f(x)= 1/8 (y+1) for 2<y<4 , 0 elsewhere
2. (a) if x takes on the values 0,1,2and 3 with probabilities 1/125, 12/125, 48/125, and 64/125, find E(x)and E(x^2)
(b) use the results of part (a) to determine the value of E[(3x+2)^2]
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1. find the expected value of the random variable y whose probability density is given by f(x)= 1/8 (y+1) for 2<y<4 , 0 elsewhere
E(y)= [y=2 to 4]∫y*f(y)dy= [y=2 to 4]∫1/8y (y+1)dy=[y=2 to 4]{y^3/24+y^2/16}=(64/24+1)-(8/24+4/16)=37/12
2. (a) if x takes on the values 0,1,2and 3 with probabilities 1/125, 12/125, 48/125, and 64/125, find E(x)and E(x^2)E(x)=0* 1/125+1*12/125+2* 48/125+3* 64/125=2.4E(x^2)= 0^2* 1/125+1^2*12/125+2^2* 48/125+3^2* 64/125=6.24
(b) use the results of part (a) to determine the value of E[(3x+2)^2]E[(3x+2)^2]=E(9x^2+12x+4)=9E(x^2)+12E(x)+4=9*6.24+12*2.4+4=88.96