Question

I would be very happy if you solve both questions. Please also round all your numerical answers to numbers of the 5-digit ?oating-point arithmetic FPA5.

1. (Repeated Independent Trials: Random Variables: Espectations). A cube has 1 red face, 2 green faces, and 3 blue faces. A game costs of rolling the cube twice independently). A player pays $1 to play. If both faces are of the same color, he is paid $2.68 (that is he wins $1.68). If not, he loses the $1 it costs to play. (1) Find the probability p that the player wins the game (ii) Use (t) to find the expected value of the game, and to determine whether the same is: (a) favorable to the player; (b) unfavorable to the player; (c) fair. 2. Bernoulli Trial Binomial Distribution). (1) Determine the expected timber of boys in a family with 6 children, assuming the sex distribution to be equally probable (an experiment with n=6 Bernouilt trials, p = 1/2). What is the probability that the expected number of boys does occur? (Here and below, aby sequence of Bernoull trials istmed to be independent) (1) One survey showed that 67% of respondents thought that they had healthy eating habits. Based on this information, we would like to find the probability that for a random sample of 10 people, 5 have healthy eating habits an experiment with n = 10 Bernoulli trials, p =?). () The probability is 0.024 that an item produced by a factory is defective. A shipment of 9285 items is sent to its warehouse (an experiment with n =? Bernoulli trials, p=?). Find the expected member of defective items and the corresponding standard deviation (iv) The probability of hitting a target per shot is 0.26. How many shots must be fired to make the probability at least 0.95 that the target will be hit?

Answer 1

According to the guidelines of Chegg it is only required to answer the first question.

was R. G. and is represent rolling red, gren and blue trece respectively. The sample of rolling two cubes independantly is: (R,R), CR,G), CR,G), CR, B, CR,8) CR,B), (GR) (G,G),(G,G), CG,B), (GB) (G,B), (GR), CG,G), CG, G) CGB), (GB), (GB) (B,C), (B,C),(6,4), (8,8), CB,B), (8,8), CB,R), CB,G), (B,G), CB,B), CB,B), (B,B), CB, R), (8,6), (8,4), (B,B),(BB), (3.8). Probability that player wins the game; p = No. of times same faces rolled out in the sample space - Size of sample space. i) Expected value of the game, E=P, X + P₂ X₂ where P, = Probability that he wins = 0.89.

P2 = Probability that he luses = 1-0.389 -0.611 x. - Value of winning - 1.68 X₂ = Value of losing out E = 0.389* 1.66 + 0.6118-1 = $0.06252 Since the expected value is positive if indica, fer a profit to the player, ce, a) favourable to the player