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:

a. Y has a binomial distribution
b. E(Z) = 20
c. P(Y=5) = (25) (0.05)5 (0.95) 20
d. X3 has a Bernoulli distribution
e. E(Z) = 250E(X₁)
f. Z has a geometric distribution
g. E(Y) = 20
h. E(X5) = 0.25
i. X₁ has a geometric distribution