Suppose the random variables X, Y, Z are obtained by spinning the adjoining roulette wheel, with X given by the outermost circle, Y given by the intermediate circle and Z given by the inner circle. (a) Calculate E[Z] (the expectation of Z). (b) Calculate E[X + YJ. (c) Calculate E[X • Z]. Is any of the three random variables X, Y, Z dependent on another? Justify your answer. (e) Are any of the three pairs (X, Y), (X, Z), (Y, Z) independent? If so, which? Justify your answer. (1) Compute P[Y=4 | Z=1]. (g) Compute E[Y|Z=1]. ( 2 .5 -3 1/6 1/12 | 1/12

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x

yes the total will be same because in both of them the expression.is rearranged but their sign remains the same hence it hss just been shuffled

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)