Continuing the last question what is the variance of

16. Continuing the last question, what is the variance of X ?
(a) 25/3
(b) 10
(c) 25
(d) 100
(e) none of the above
17. Let Z be a standard normal random variable, Φ the standard normal cdf, and c an arbitrary
positive number. Which of the following expressions is false ? (Hint: draw a picture.)
18. Let Z be a standard normal random variable, Φ the standard normal cdf, and c an arbitrary
positive number. Which of the following quantities is larger than the others?
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19. Let X be a normal random variable with mean 85 and standard deviation 10. Knowing that
Φ(1 . 5) = 0 . 9332, what is the probability that X ≥ 70?
20. Let X be the time (hours) between two successive arrivals at the drive-up window of a local
bank. Suppose X follows an exponential distribution with λ = 1; so the cdf of X is given by
F ( x ) =
(
0 x < 0
1 - e
- x
x ≥ 0
Given that the last arrival occurred half an hour ago, what is the probability that no one else
will arrive within the next half hour?
(a) e
- 1
(b) 1 - e
- 1
(c) e
- 1 / 2
(d) 1 - e
- 1 / 2
(e) none of the above
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