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

figure c

step-by-step explanation:

hope this .

29933333.33

step-by-step explanation:

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: