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Answer the following questions: The team A has a winning probability whenever it plays. If the...
In 29 of the first 52 Super Bowl games in professional football (56%), the winning team...
In 29 of the first 52 Super Bowl games in professional football (56%), the winning team won by over 9 points (double digits). Suppose we randomly select 10 Super Bowl games out of the first 52 and count the number in which the winning team had a double digit victory. Assume independence between the Super Bowls selected- consider them to be chosen with replacement. a) Define the random variable, x, and give the name and important parameters of the probability...
A discrete random variable X has the following probability distribution:
A discrete random variable X has the following probability distribution: x7778798081 P(x) 0.150.150.200.400.10Compute each of the following quantities. i. P(X = 80) ii. P(x > 80) iii. P(X ≤ 80) iv. The mean, μ of x. v. The variance, σ2 of X. vi. The standard deviation, σ of X.
Continuous random variable
(e) A continuous random variable X has the probability density function given by: f(x) = ( 2x/√ k for 0 ≤ x ≤ 2 0 otherwise. i. Show that the constant k equals 16. ii. Find the expected value of X. iii. Find the variance of X. iv. Derive the cumulative distribution function, F(x). v. Calculate P(X < 1 | X < 1.5)
[2] [3] (5) (a) A soccer squad contains 3 goalkeepers, 7 defenders, 9 midfielders and 4...
[2] [3] (5) (a) A soccer squad contains 3 goalkeepers, 7 defenders, 9 midfielders and 4 forwards. (i) In how many ways can a team of 1 goalkeeper, 4 defenders, 4 midfielders, and 2 attackers be chosen from this squad? (ii) Two of the defenders refuse to play together. In how many ways can a team be chosen that contains at most one of these two defenders? (b) Let p and q be real numbers. A random variable X has...
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Question # 7 A random variable x has the following distribution: px) 0. -2 -1 0 +1 +2 +3 0.2 k 0.3 2k (i) Find k. (ii) Find P(x <0). (iii) Find P Answer-hints: (iii) P(-2 < x < +2) = 0.8; (v) E11-1.01 2 x +2). (iv) Plot CDF of x; and (v) Find E[x]
For each of the following questions: clearly indicate the probability distribution being used to solve the...
For each of the following questions: clearly indicate the probability distribution being used to solve the problem solve by hand, and verify your answer using MATLAB. 1. Two teams, A and B, play a series of games. If team B has a probability 0.4 of winning each game, is it to their advantage to play the best three out of five games or the best four out of seven, and why? Assume the outcomes of successive games are independent. 2....
A hockey team plays in an arena that has a seating capacity of 15,000 spectators. With...
A hockey team plays in an arena that has a seating capacity of 15,000 spectators. With the ticket price set at $14, average attendance at recent games has been 9500. A market survey indicates that for each dollar the ticket price is lowered, the average attendance increases by 1000. Find the ticket price that maximizes revenue from ticket sales. Recall that revenue is: ticket price x Attendance Enter the exact value of the ticket price. Answer An open-top box is...
2.1 Let X be a discrete random variable with the following probability distribution Xi 0 2 4 6 7 P(X =...
2.1 Let X be a discrete random variable with the following probability distribution Xi 0 2 4 6 7 P(X = xi) 0.15 0.2 0.1 0.25 0.3 a) find P(X = 2 given that X < 5) b) if Y = (2 - X)2 , i. Construct the probability distribution of Y. ii. Find the expected value of Y iii. Find the variance of Y
BSP2014 5. Given xe 20 Cr) 0 x<0 i) Show thatAx) is a pdf. ii) Find...
BSP2014 5. Given xe 20 Cr) 0 x<0 i) Show thatAx) is a pdf. ii) Find the cumulative distribution function (CDF) of X 6. The p.d.fof a random variable Y is given by y +1 for2<y<4 v) 0 elsewhere Find i) the value of c ii) P(Y<3.2) iii)P(2.9 < γ< 3.2) 7. The p.d.fof a random variable X is given by elsewhere i) Find P(X<1.5) ii) Find P(0.5 X1.5)
For each of the following functions, (i) find the constant c so that f(x) is a...
For each of the following functions, (i) find the constant c so that f(x) is a pdf of a random variable x, (ii) find the cdf F(x)-P(XSX), (iii) sketch graphs of the pdf f (x) and the distribution function F(x), and (iv) find μ and σ2. (a) f (x) x3/4, 0 <x<c (b) f (x)-(3/16x-,-c < x c
[2] [3] (5) (a) A soccer squad contains 3 goalkeepers, 7 defenders, 9 midfielders and 4 forwards. (i) In how many ways can a team of 1 goalkeeper, 4 defenders, 4 midfielders, and 2 attackers be chosen from this squad? (ii) Two of the defenders refuse to play together. In how many ways can a team be chosen that contains at most one of these two defenders? (b) Let p and q be real numbers. A random variable X has...
Need all parts some hints are giving ! If you don’t know
don’t answer need experts only
Question # 7 A random variable x has the following distribution: px) 0. -2 -1 0 +1 +2 +3 0.2 k 0.3 2k (i) Find k. (ii) Find P(x <0). (iii) Find P Answer-hints: (iii) P(-2 < x < +2) = 0.8; (v) E11-1.01 2 x +2). (iv) Plot CDF of x; and (v) Find E[x]
For each of the following questions: clearly indicate the probability distribution being used to solve the problem solve by hand, and verify your answer using MATLAB. 1. Two teams, A and B, play a series of games. If team B has a probability 0.4 of winning each game, is it to their advantage to play the best three out of five games or the best four out of seven, and why? Assume the outcomes of successive games are independent. 2....
A hockey team plays in an arena that has a seating capacity of 15,000 spectators. With the ticket price set at $14, average attendance at recent games has been 9500. A market survey indicates that for each dollar the ticket price is lowered, the average attendance increases by 1000. Find the ticket price that maximizes revenue from ticket sales. Recall that revenue is: ticket price x Attendance Enter the exact value of the ticket price. Answer An open-top box is...
BSP2014 5. Given xe 20 Cr) 0 x<0 i) Show thatAx) is a pdf. ii) Find the cumulative distribution function (CDF) of X 6. The p.d.fof a random variable Y is given by y +1 for2<y<4 v) 0 elsewhere Find i) the value of c ii) P(Y<3.2) iii)P(2.9 < γ< 3.2) 7. The p.d.fof a random variable X is given by elsewhere i) Find P(X<1.5) ii) Find P(0.5 X1.5)
For each of the following functions, (i) find the constant c so that f(x) is a pdf of a random variable x, (ii) find the cdf F(x)-P(XSX), (iii) sketch graphs of the pdf f (x) and the distribution function F(x), and (iv) find μ and σ2. (a) f (x) x3/4, 0 <x<c (b) f (x)-(3/16x-,-c < x c
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