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probability考试代写 STAT/MATH 395代写

2022-03-28 14:53 星期一 所属: 统计代写 浏览:207

probability考试代写

STAT/MATH 395

Midterm Exam

probability考试代写 We draw a ball from the urn repeatedly with replacement until we see the first green or yellow ball, and then we stop.

Exercise 1.   probability考试代写

An urn contains contains 5 balls: 3 green, 1 yellow and 1 white ones. We draw a ball from the urn repeatedly with replacement until we see the first green or yellow ball, and then we stop. Let X denote the number of draws we needed. Let Y equal to 1 if the last draw is green and 2 if the last draw is yellow.

  1. Find the joint distribution of (X, Y ). You can leave your results with combination terms. Hint: consider Y = 1 and Y = 2
  2. Find the marginal mass function ofX.
  3. Find the marginal mass function of Y.
  4. X and Yindependent?
probability考试代写
probability考试代写

Exercise 2.   probability考试代写

The joint density of X and Y is given by

f (x, y) = 1 (y  x)ey, y < x < y, < y < 

  1. Find the density function ofX.
  2. Find the density function of Y.
  3. Are X and Yindependent?

Exercise 3.  probability考试代写

Let X1, X2 be independent Exp(λ) random variables. Let U = X1 + X2, V = X1 X2.

  1. What is the joint pdf of U, V?
  2. What is the marginal pdf of V?
  3. Are U, Vindependent?
probability考试代写
probability考试代写

 

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