iPad @ 70% 5:34 PM a bbhosted.cuny.edu 13. The cumulative distribution function,
ID: 3326679 • Letter: I
Question
iPad @ 70% 5:34 PM a bbhosted.cuny.edu 13. The cumulative distribution function, denoted as F(x) in both cases of continuous and discrete random variables, gives the probability that the random variable is less than or equal to 14. A binomial random variable has an expected value equal to and variance equal to 15. One thousand tickets are sold at $3 each. One ticket will be randomly selected and the winner will receive a color television valued at $387. What is the expected value for a person that buys one ticket? 16. In another raffle, 1000 tickets are sold for $5 each. One ticket will be randomly selected whereby the winner receives $1700. What is the expected value for a person that buys one ticket? Find the standard deviation of the binomial distribution for a sample where n = 2000 and p = 0.74. (p = success rate) 18. A standardized test consists of 400 multiple choice questions (A to E). If someone guesses on all the questions, what is the mean number of correct answers? 19. A test consists of 200 multiple choice questions (A to E) and only one is the correct choice. Find the mean and the standard deviation of the number of correct answers.Explanation / Answer
Question 13:
The cumulative distributive function for X is computed as:
F(x) = P(X <= x)
Therefore x is the required answer here.
Question 14:
If a binomial distribution is defined with the parameters n and p then the expected value of a binomial variable is given as: np and the variance is given as: np(1-p)
Question 15:
Expected value for a person that buys the ticket is computed here as:
= - Cost of one ticket + 387*Probability to win the ticket
= -3 + 387/1000
= -2.613
Therefore the expected value here is -$2.613
Question 16
Expected value for a person that buys the ticket is computed here as:
= - Cost of one ticket + 1700*Probability to win the ticket
= -5 + 1700/1000
= -3.3
Therefore the expected value here is -$3.3
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