Additional Extra Problems From Ch. 7
1)
Using the joint pdf of Problem 7.40 on p. 381 of Ross,
obtain E(Y|X = x), for x > 0, expressing your answer as a simple function of x.
Show adequate work to justify your answer.
2)
Do Problem 7.41 on p. 381 of Ross, just for the case of j = 1.
Provide justification for your answer.
3)
Do part (a) of Problem 7.69 on p. 384 of Ross,
except let
μ1 =
σ1 = 1,
μ2 =
σ2 = 2, and p = 0.5.
Show adequate work to justify your answer.
4)
Do part (a) of Problem 7.60 on p. 382 of Ross, except put p = 1/3.
Provide justification for your answer.
5)
Do part (a) of Problem 7.66 on p. 384, except put p = 1/2, and assume F(x) = 1/2.
Provide justification for your answer.
6)
Do part (b) of Problem 7.69 on p. 384 of Ross,
except let
μ1 =
σ1 = 1,
μ2 =
σ2 = 2, and p = 0.5.
(Note: The σi are standard deviations, not variances.)
Show adequate work to justify your answer.
7) Do parts (a), (b), and (c) of Problem 7.80 on p. 385 of Ross.
(Hint: For all three parts, I recommend using the tables on pages 364 and 365 of the text to identify the
distributions of X and Y from the mgfs,and not using the mgfs for anything else. (So while the mgfs should be used to
identify the distributions, they shouldn't be used to obtain the probabilities. They could be used to obtain the expected values of the
random variables, but it's not necessary to do so.))