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Week 2 Homework
Due Jan 30 at 11:59pm Points 11 Questions 11 Available Jan 23 at 8am - Feb 2 at 11:59pm Time Limit None
Instructions
This quiz was locked Feb 2 at 11:59pm.
Attempt History
Attempt Time Score LATEST Attempt 1 2,799 minutes 11 out of 11
Score for this quiz: 11 out of 11 Submitted Jan 30 at 11:43pm This attempt took 2,799 minutes. Correct answer
Question 1 1 / 1 pts
a. 0. b. 0.
You could also have used a binomial distribution argument to solve this problem, i.e.,
c. 0. d. 0.
Please answer all the questions below.
(Lesson 2.5: Probability Basics.) If and and are independent, find the probability that exactly one of and occurs.
e. I'm from The University Of Georgia. Is the answer -3?
The answer is (b). To see why, note that
You could also have used a binomial distribution argument to solve this problem, i.e.,
Correct answer
Question 2 1 / 1 pts
a. 5/ Write out every possible outcome explicitly, or use the following binomial argument: Let denote the number of times a "4" comes up. Clearly,
b. 1/ c. 13/ d. 1/
(a). Write out every possible outcome explicitly, or use the following binomial argument: Let denote the number of times a "4" comes up. Clearly,
Correct answer
Question 3 1 / 1 pts
a. - b. 3 c. 1
(Lesson 2.5: Probability Basics.) Toss 3 dice. What's the probability that a "4" will come up exactly twice?
(Lesson 2.7: Great Expectations.) Suppose that is a discrete random variable having with probability 0.2, and with probability 0.8. Find.
Finally, by LOTUS,
so that. So the answer is (d).
Correct answer
Question 6 1 / 1 pts
a. 2/ b. 1 c. 3/ d. 2
By LOTUS,
(d) By LOTUS,
Correct answer
Question 7 1 / 1 pts
a. b. c. This follows because
No other possible values for.
d.
(Lesson 2.7: Great Expectations.) Suppose X is a continuous random variable with p.d.f. for. Find.
(Lesson 2.8: Functions of a Random Variable.) Suppose is the result of a 5-sided die toss having sides numbered. Find the probability mass function of.
(c). This follows because
No other possible values for. Correct answer
Question 8 1 / 1 pts
a. , for Note that the c.d.f. of is (you can do this in your head). So by the Inverse Transform Theorem, we immediately have that is Unif(0,1), with the p.d.f. . b. , for c. , for d. , for
(a). Note that the c.d.f. of is (you can do this in your head). So by the Inverse Transform Theorem, we immediately have that is Unif(0,1), with the p.d.f. .
Correct answer
Question 9 1 / 1 pts
a. 1 b. 1/ c. 1/ d. 1/
(Lesson 2.8: Functions of a Random Variable.) Suppose is a continuous random variable with p.d.f. for. Find the p.d.f.. (This may be easier than you think.)
(Lesson 2.9: Jointly Distributed RVs.) Suppose that for. Find .
NO! The lesson has a theorem that says that , are independent if and only if you can write with no funny limits for some functions and. Can't do such a factorization, so and ain't indep.
Quiz Score: 11 out of 11
