Let X and Y be joint continuous random variables with joint density function fpx, yq " # e ´y y 0 ă x ă y, 0 ă y ă 8 0 otherwise Compute ErX2 | Y " ys. Hint: Start with ErX2 | Y " ys " ż y 0 x 2 fX|Y px |

For X, the parameter

is λX = 1/2 and for Y it is λY = 1. Using the formula sheet, Mean is

E[Z] = E[X] + 2E[Y ] = 4. Variance is V ar(Z) = V ar(X) + 4V ar(Y ) = 8.

lo.lll

step-by-step explanation:

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)