Ivan Pedroso is a long jump athlete who wishes to qualify for the upcoming Summer Olympics. The olympic qualifying standard is 8.22 m in men's long jump, so a jump is considered as successful if it is equal to 8.22 m or more. Suppose that at each jump, Pedroso has a 0.05 chance of jumping successfully. Assume that all jumps are independent. For j= 1,2,3,...Let X; be the random variable that equals 1 if Pedroso jumps successfully at jth jump, and equals 0 otherwise. Let Y be the trial number where Pedroso jumps successfully for the first time, and let Z be the total number of successful jumps out of the first 250 trials. Which of the following is true? Select one or more: O a. P(Y = 5) = 0.05) (0.95)20 O b. E(Z) = 250E(X1) O. Z has a geometric distribution O d. E(Y) = 20 O e. E(Z) =20 O f. Y has a binomial distribution Og. x, has a geometric distribution O h. (X_3 \) has a Bernoulli distribution Oi. V E(X_5)=0.25 \)
Ivan Pedroso is a long jump athlete who wishes to qualify for the upcoming Summer Olympics. The olympic qualifying standard is 8.22 m in men's long jump, so a jump is considered as successful if it is equal to 8.22 m or more. Suppose that at each jump, Pedroso has a 0.05 chance of jumping successfully. Assume that all jumps are independent. For j= 1,2,3,...Let X; be the random variable that equals 1 if Pedroso jumps successfully at jth jump, and equals 0 otherwise. Let Y be the trial number where Pedroso jumps successfully for the first time, and let Z be the total number of successful jumps out of the first 250 trials. Which of the following is true? Select one or more: O a. P(Y = 5) = 0.05) (0.95)20 O b. E(Z) = 250E(X1) O. Z has a geometric distribution O d. E(Y) = 20 O e. E(Z) =20 O f. Y has a binomial distribution Og. x, has a geometric distribution O h. (X_3 \) has a Bernoulli distribution Oi. V E(X_5)=0.25 \)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Ivan Pedroso is a long jump athlete who wishes to qualify for the upcoming Summer Olympics. The olympic qualifying standard is 8.22 m in men's long jump,
so a jump is considered as successful if it is equal to 8.22 m or more. Suppose that at each jump, Pedroso has a 0.05 chance of jumping successfully. Assume
that all jumps are independent. For j= 1,2,3,...Let X; be the random variable that equals 1 if Pedroso jumps successfully at jth jump, and equals 0
otherwise. Let Y be the trial number where Pedroso jumps successfully for the first time, and let Z be the total number of successful jumps out of the first
250 trials. Which of the following is true?
Select one or more:
O a. P(Y = 5) = ()(0.05) (0.95)20
O b. E(Z) = 250E(X1)
O c. Z has a geometric distribution
O d. E(Y) = 20
O e. E(Z) = 20
O f. Y has a binomial distribution
Og. X, has a geometric distribution
O h. (X_3 \) has a Bernoulli distribution
Oi. (E(X_5)=0.25 \)
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