CAS MA 581: Probability
Midterm 2
概率考试代考 Note: No cheat sheet, notes, or textbook allowed. You are allowed to use a calculator. Please start a new page for each problem (not for individual
Note: 概率考试代考
- No cheat sheet, notes, or textbook allowed. You are allowed to use a calculator.
- Please start a new page for each problem (not for individual parts of each problem) and specify the pages for the corresponding problems when uploading your solutions to Gradescope.
- Please show your work and complete the exam independently.
- This exam contains 3 problems in 1 page.
(a) (5 points) Find the marginal PDF for X.
(b) (5 points) Find the marginal PDF for Y .
(c) (5 points) Show that X and Y are not independent.
2. 概率考试代考
The random variable X has the PDF
(a) (5 points) Determine the value of c.
(b) (5 points) Let A be the event {X ≤ 1}. Find the conditional PDF fX|A(x).
(c) (5 points) Let A be the same event as in part (b). Find var(X|A).
(d) (5 points) Let Y = √|X|. Find the PDF of the random variable Y .
3.(15 points) 概率考试代考
Let X and Y be independent random variables that are uniformly distributed on the interval [0, 1]. What is the PDF of the random variable Z = (3Y )/X?
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