Question

5.) In the game of Roulette described above you can also bet on a color. For example, 18 of the 38 numbers are red and you can bet $1 that the wheel will land on a red number. If a red number does not come up the casino pays you nothing while if a red number does come up the casino pays you $2. Remember in calculating your profit that you started by paying the casino $1. If you bet on red, (a) calculate the probability that the winning number is red. (b) calculuate the probability that the winning number is not red. (c) find your expected profit. (d) find the variance and standard deviation of your profit. (e) Compare the expected profit when you bet on red to the expected profit when you bet on one specific number as calculated in question 4 (1) Similarly, compare the variances and standard deviations of the profit when you bet on red versus betting on a single number. Recalling that the variance and standard deviation measure the dispersion of the values of the random variable, do you prefer to bet on red or do you prefer to bet on a single number? Explain why.

Answer 1

a)

there are 18 red out of 38

hence p(winning number is red) = 18/38

b)

probability that winning number is not red = 1- p(winning number is red)

= 1 -18/38

= 20/38

c)

X = profit

P(X = -1) = 20/38 {when winning number is not red}

P(X = 1) = 18/38 {winning number is red}

x	p	x*p	p*x^2
-1	0.526316	-0.52632	0.526316
1	0.473684	0.473684	0.473684
		E(X)	E(X^2)
		-0.05263	1

E(X) = sum P(X = xi) xi

= -0.05263

d)

Var(X) = E(X^2) - E(X)^2

= 1 - (-0.05263)^2

= 0.99723

sd (X) = sqrt(Var(X)) = sqrt(0.99723 ) = 0.998614

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By HOMEWORKLIB RULES, we have to answer only first 4 sub-parts in multiple sub-parts

Please post rest questions again

Also there is reference to Q4, so post it too