You are ex pected to win $3.65 per play. c. Find the standard deviation of the payoff and interpret this value in context. (3 pts.) Ox= 2+10-3.65)².3t (5-3,45)*. 5a+ (0-3.65)², 365...

3b

Extracted text: You are ex pected to win $3.65 per play. c. Find the standard deviation of the payoff and interpret this value in context. (3 pts.) Ox= 2+10-3.65)².3t (5-3,45)*. 5a+ (0-3.65)², 365 Ox=V78.52+2.32+0.42+9.22 There is a possibilitu of an increase Ox= 13.8 d. What is the probability that a player will win more than they bet initially? decrease of $13.8 from the u per play 2 of 2 e. Suppose that the player wanted to make 4 bets. What would be the new expected payoff? What would be the new standard deviation? Mx =9 Tx=Jia3(1-1952) p= 16/5n ux= 1.23 Ox=0.92 2. Picard Partners is planning a major investment. The amount of profit X is uncertain but a probabilistic estimate gives the following distribution (in millions of dollars): Profit [ Frobability 0.1 0.2 6. | 10 0.4 0.2 | 0.1 (a) Find the mean profit uy and the standard deviation of the profit. Mx = (0.) + 1.5(0.2) + 2 (0.4) 4(0.5)+io(0.1) llx=3 O=)?.0.1+(1.5-3)*.0,2 +(a-3)^-0mel4-3)*,0,2+(10-3)*-0. Ox=V0.M+0.45+0.4+0.2-49 0x=2.52 (b) Picard Partners owes its source of capital a fee of $200,000 plus 10% of the profits X. So the firm actually retains Y 0.9X- 0.2 from the investment. Find the mean and standard deviation of Y. Y-Ó.9(3)-0,2 y=0,9(2.52) 9=2.5 4= 2268 3. Mr. Voss and Mr. Cull bowl every Tuesday night. Over the past few years, Mr. Voss's scores have been approximately Normally distributed with a mean of 212 and a standard deviation of 31. During the same period, Mr. Cull's scores have also been approximately Normally distributed with a mean of 230 and a standard deviation of 40. a. Assuming their scores are independent, what is the probability that Mr. Voss scores higher than Mr. Cull on a randomly-selected Tuesday night? Mv-e=212-230--18 2: 0+18 Ov-e= 312+402 Ov-e=JasGI Ou-e= 50.6 50,6 2=0.36 normaledf lower:0.36 upper:co M:0 0:1 0.359 b. Assuming their scores are independent, what is the probability that Mr. Cull scores more than 50 points higher than Mr. Voss on a randomly-selected Tuesday night?