Additional Extra Problems From Ch. 5
1)
Consider the random variable X of Problem 5.14 on p. 229 of Ross.
Give the value of E(X 4), using whatever legitimate method you wish to use.
Show some work,
and give an exact numerical value (either expressed as a fraction or expressed in decimal form).
2)
Consider the random variable X of Problem 5.15 on p. 229 of Ross.
Use a table of the standard normal distribution cdf or else appropriate software to obtain values, rounded to the
nearest thousandth, for the probabilities indicated below. (If you use a table, you should use linear interpolation
if you need the probability for a value for which the probability is not given in the table.)
- (a) P(X < 2)
- (b) P(X > 18)
- (c) P(10 < X < 18)
3)
Consider the random variable X of Problem 5.4 on p. 228 of Ross.
Let U be a uniform (0, 1) random variable.
Give a function of U which has the same distribution as X.
Provide work to justify your answer.
4)
Do Problem 5.25 on p. 230 of Ross. Show some work,
and give a numerical value, rounded to 3 significant digits, for the desired approximate probability.
(Note: Doing an exact computation of the desired binomial distribution probability is not unreasonable here,
but I want you to give the approximate probability which results from using a normal approximation with a continuity
correction. (You can obtain the exact probability as a partial check of your work.))