Extra Problems From Ch. 4
1)
Do parts (a) and (b) of Problem 4.35 on p. 178 of Ross, except change the number of marbles of each color from 5 to 4.
Provide justification for your answers.
2)
Do parts (a) and (b) of Problem 4.39 on p. 178 of Ross.
Provide justification for your answers.
(Note: While part (b) is rather straightforward and easy, part (a) isn't nearly as trivial.)
3)
Do Problem 4.42 on p. 178 of Ross.
(Be sure to note that the desired probability is that he gets at least 7 out of 10 correct just by guessing (with each coin flip
matching his guess with probability 1/2, independent of the results from previous coin flips).)
4)
Consider Problem 4.44 on p. 179 of Ross. Make an assumption of independent errors and give the probability that the majority of the
5 digits will be incorrectly received.
Show adequate work
to justify your answer.
5)
Do part (a) of Problem 4.50 on p. 179 of Ross.
Show adequate work to justify your answer.
6)
Do parts (a) and (b) of Problem 4.74 on p. 181 of Ross, except suppose that Smith always bets on the number 36 (and so has a
probability of 1/38 of winning each time he makes the bet). (Note: The probability is 1/38 (and not 1/36).)
Show adequate work to justify your answer.
7)
If X is a Bernoulli (p) random variable, and Var(2X) = 2Var(X), what can be said about the value of p?
Be as specifc as possible, and provide some justification for your answer.