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Concept explainers
Sagittarius Casino
The Sagittarius Casino's strategy for establishing a competitive advantage over its competitors is to create unique and interesting new games for its customers to play. Sagittarius management feels it is time for the casino to once again introduce a new game to excite its customer base, and Sagittarius' s Director of Research and development, Lou Zerbit, believes he and his staff have developed a new game that will accomplish this goal. The game, which they have named POSO! (an acronym for Payouts On Selected Outcomes), is to be played in the following manner. A player will select two different values from 1, 2, 3, 4, 5, and 6. Two dice are then rolled. If the first number the player selected comes up on at least one of the two dice, the player wins $5.00; if the second number the player selected comes up on both of the dice, the player wins $10.00. If neither of these
For example, suppose a player fills out the following card for one game of POSO!
When the two dice are rolled, if at least one die comes up 4 the player will win $5.00, if both dice come up 2 the player will win $10.00, and if any other outcome occurs the player wins nothing.
Managerial Report
Sagittarius management now has three questions about POSO! These questions should be addressed in your report.
3. Sagittarius managers want to take in more than they pay out on average for a game of POSO!. Furthermore, casinos such as Sagittarius are often looking for games that provide their gamers with an opportunity to play for a small bet, and Sagittarius management would like to charge players $2.00 to play one game of POSO!. What will be the expected profit earned by Sagittarius Casino on a single play if a player has to pay $2.00 for a single play of POSO!? Will Sagittarius Casino expect to earn or lose money on POSO! if a player pays $2.00 for a single play? What is the minimum amount Sagittarius Casino can charge a player for a single play of POSO! and still expect to earn money?
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Chapter 5 Solutions
Essentials of Modern Business Statistics with Microsoft Office Excel (Book Only)
- Theorem 2.6 (The Minkowski inequality) Let p≥1. Suppose that X and Y are random variables, such that E|X|P <∞ and E|Y P <00. Then X+YpX+Yparrow_forwardTheorem 1.2 (1) Suppose that P(|X|≤b) = 1 for some b > 0, that EX = 0, and set Var X = 0². Then, for 0 0, P(X > x) ≤e-x+1²² P(|X|>x) ≤2e-1x+1²² (ii) Let X1, X2...., Xn be independent random variables with mean 0, suppose that P(X ≤b) = 1 for all k, and set oσ = Var X. Then, for x > 0. and 0x) ≤2 exp Σ k=1 (iii) If, in addition, X1, X2, X, are identically distributed, then P(S|x) ≤2 expl-tx+nt²o).arrow_forwardTheorem 5.1 (Jensen's inequality) state without proof the Jensen's Ineg. Let X be a random variable, g a convex function, and suppose that X and g(X) are integrable. Then g(EX) < Eg(X).arrow_forward
- Can social media mistakes hurt your chances of finding a job? According to a survey of 1,000 hiring managers across many different industries, 76% claim that they use social media sites to research prospective candidates for any job. Calculate the probabilities of the following events. (Round your answers to three decimal places.) answer parts a-c. a) Out of 30 job listings, at least 19 will conduct social media screening. b) Out of 30 job listings, fewer than 17 will conduct social media screening. c) Out of 30 job listings, exactly between 19 and 22 (including 19 and 22) will conduct social media screening. show all steps for probabilities please. answer parts a-c.arrow_forwardQuestion: we know that for rt. (x+ys s ا. 13. rs. and my so using this, show that it vye and EIXI, EIYO This : E (IX + Y) ≤2" (EIX (" + Ely!")arrow_forwardTheorem 2.4 (The Hölder inequality) Let p+q=1. If E|X|P < ∞ and E|Y| < ∞, then . |EXY ≤ E|XY|||X|| ||||qarrow_forward
- Theorem 7.6 (Etemadi's inequality) Let X1, X2, X, be independent random variables. Then, for all x > 0, P(max |S|>3x) ≤3 max P(S| > x). Isk≤narrow_forwardTheorem 7.2 Suppose that E X = 0 for all k, that Var X = 0} x) ≤ 2P(S>x 1≤k≤n S√2), -S√2). P(max Sk>x) ≤ 2P(|S|>x- 1arrow_forwardThree players (one divider and two choosers) are going to divide a cake fairly using the lone divider method. The divider cuts the cake into three slices (s1, s2, and s3).If the chooser's declarations are Chooser 1: {s3} and Chooser 2: {s3}, which of the following is a fair division of the cake?arrow_forwardTheorem 1.4 (Chebyshev's inequality) (i) Suppose that Var X x)≤- x > 0. 2 (ii) If X1, X2,..., X, are independent with mean 0 and finite variances, then Στη Var Xe P(|Sn| > x)≤ x > 0. (iii) If, in addition, X1, X2, Xn are identically distributed, then nVar Xi P(|Sn> x) ≤ x > 0. x²arrow_forwardTheorem 2.5 (The Lyapounov inequality) For 0arrow_forwardTheorem 1.6 (The Kolmogorov inequality) Let X1, X2, Xn be independent random variables with mean 0 and suppose that Var Xk 0, P(max Sk>x) ≤ Isk≤n Σ-Var X In particular, if X1, X2,..., X, are identically distributed, then P(max Sx) ≤ Isk≤n nVar X₁ x2arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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