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美国统计代写推荐 Stat 351代写 statistics代写

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美国统计代写推荐

Stat 351 Fall 2021

美国统计代写推荐 Suppose that X1, X2, and X3 are independent and identically distributed continuous random variables with common density function f(x).

Assignment 1

Each question is worth 10 marks for a total of 40 marks. Question 5 is a bonus question.

1.  美国统计代写推荐

Let X and Y be independent random variables with X ~U (1,3) and Y~N (0,1).

(a)Determine ,( , ), the joint distribution function of (X, Y)’.

(b)Show directly (by computing the  indicated partialderivative) that:

(c)Is this surprising? Why or whynot?

(d)If Z~𝐸𝑥p(4).is independent of X and Y, determine the joint density of (X, Y, Z)’.

2.

Suppose that X~N (0,1). Let Y be independent of X with P(Y = 1) = P(Y = -1) = 1/2. Define the random variable Z be setting Z = XY.

(a)ComputeCov(X,Z).

(b)(Showthat P(Z >= 1) = P(X >= 1). Use this fact to conclude that Z and X are NOT   independent.  美国统计代写推荐

(c)Generalizepart (b) to show that P(Z >= x) = P(X >= x) for every . This implies that Z~N (0,1)

美国统计代写推荐
美国统计代写推荐

3.  美国统计代写推荐

Let (X, Y) be a point that is uniformly distributed on a square whose corners are (±1, ±1). Determine the distribution(s) of the x- and y-coordinates. Are X and Y independent? Are they uncorrelated?{Exercise 1.3. p19}. See example 1.1.

4.

Suppose that X1, X2, and X3 are independent and identically distributed continuous random variables with common density function f(x).

(a)Compute P(X1 >X2)

(b)Compute P(X1 > X2| X1 >X3)

(c)Compute P(X1 > X2| X1 <X2)

Hint: You can answer this problem easily using symmetry.

5.Bonus  美国统计代写推荐

Let (X, Y, Z) be a point chosen uniformly within the three-dimensional unit sphere. Determine the marginal distributions of (X, Y) and X.

{Exercise 1.1. p18}

Finding the marginal distribution of (X, Y)’ involves a computation similar to Example 1.1. However, finding the marginal distribution of just X is much more frustrating.

美国统计代写推荐
美国统计代写推荐

 

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