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Chapter 5: Q.5.4 (page 215)
Prove Corollary.
Therefore,
Hence Proved.
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Repeat Problem when the ball selected is replaced in the urn before the next selection.
For some constant c, the random variable X has the probability density function f(x) = c x n 0 < x < 1 0 otherwise Find (a) c and
(b) P{X > x}, 0 < x < 1.
The median of a continuous random variable having distribution function F is that value m such that F(m) = . That is, a random variable is just as likely to be larger than its median as it is to be smaller. Find the median of X if X is
(a) uniformly distributed over (a, b);
(b) normal with parameters μ,σ;
(c) exponential with rate λ.
The lung cancer hazard rateof a -year-old male smoker is such that
Assuming that a -year-old male smoker survives all other hazards, what is the probability that he survives to
ageand age 60 without contracting lung cancer?
Jones figures that the total number of thousands of miles that an auto can be driven before it would need to be junked is an exponential random variable with a parameter. Smith has a used car that he claims has been driven only miles. If Jones purchases the car, what is the
probability that she would get at least additional miles out of it? Repeat under the assumption that the life-
time mileage of the car is not exponentially distributed, but rather is (in thousands of miles) uniformly distributed over.
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