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# 概率代考 Probability代写 Midterm代写 考试助攻

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## Midterm 2

### 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 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.

### 1. Let X and Y have joint PDF 概率代考

(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. The random variable X has the PDF 概率代考

(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 = p√|X|. Find the PDF of the random variable Y .

### 3. (15 points) 概率代考

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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