8) let X be a random variable with the following probability distribution: Find g(x), where g(x) = (2X + 1). a) Mg(x) =g(x)P(x) b) E(X) =XP(x) -xP(x) =(2*(-3)+1)*(1/6)+(2*6+1)*(1/2)+(2*9+1)*(1/3)=209 =(-3)*(1/6)+6*(1/2)+9*(1/3) =5.5 E(X)=(-3)*(1/6)+6*(1/2)+9*(1/3) =46.5 hence E(g(x) =E((2x+1)) =E(4x+1+4x) =4E(X)+E(1)+4E(X)=4*46.5+1+4*5.5=209 QUESTION 5 Find the standard deviation of the random variable g(X) = (2X+1) from Question 8 of your last homework. QUESTION 6 The length of time, in minutes, for an airplane to obtain clearance for takeoff at a certain airport is a random variable density function Y=3X-2 X where has the 1 x>0 f(x) = 4 0, elsewhere Find the variance of the random variable Y .