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Chapter 5: Q. 5.18 (page 213)
Suppose that X is a normal random variable with
mean 5. If P{X > 9} = .2, approximately what is Var(X)?
The required variance is.
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Consider the function
Could be a probability density function? If so, determine
. Repeat if were given by
localid="1646632841793"
If X is an exponential random variable with parameter 位, and c > 0, show that cX is exponential with parameter 位/c
A model for the movement of a stock supposes that if the present price of the stock is , then after one period, it will be either with probability or with probability . Assuming that successive movements are independent, approximate the probability that the stock鈥檚 price will be up at least percent after the next periods if
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 渭,蟽;
(c) exponential with rate 位.
Let X be a continuous random variable having cumulative distribution function F. Define the random variable Y by Y = F(X). Show that Y is uniformly distributed over (0, 1).
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