2. (20 pts) Let X and Y be random variables of the continuous type having the joint p.d.f.8f(x,y) = żay, 0≤x≤1, x ≤ y ≤ 2xa) Draw a graph that illustrate the domain of the joint pdf.b) Find the marginal pdfs of X and Y.c) Compute x fly.d) Compute o2, and o².e) Calculate Cov(X, Y) and p.

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Answered: 2. (20 pts) Let X and Y be random…

A First Course in Probability (10th Edition)

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Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Let X,Y ~ U(0,1) be iid. Derive the distribution of Z=X/Y
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Show the density func in table form and show complete solution.
Exercise 17. Let X₁,..., Xn~ N(u, o2) be i.i.d. where u is known, but o2 is unknown. Consider the estimate n 1 Σ(X₁-1 for the variance. a) Show that 7² C := i=1 -μ)² 72 2 ·Σ( X ₁ = μ)² ~ x² (n). O i=1 b) For a € (0, 1), denote the a-quantile of x2 (n) by qn(a). Using this notation, find numbers an, bn E R such that P(o² bno²) = 2.5%. c) Using these results, develop a test which can be used to test the hypothesis Ho: o² = o against the alternative H₁: 02 08. d) Assume we have n = 100, μ = 0 and we have observed 2 = 4.81. Test the hypothesis Ho: o² = 4 vs. H₁: o² #4 at significance level 5%.
A1 Please, show me how to compute this.
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Let Z₁ = X₁-μx ~N(0,1), and Wi σχ = Yi-HY~N(0,1), for i = 1,2,3,...,10, then: oy i) State, with parameter(s), the probability distribution of the statistic, T = ii) Find the mean and variance of the statistic T = Σt, wi? Σ, Z² Σt=1Zi 4i=1 iii) Calculate the probability that a statistic T = Z₁ + W₁ is at most 4. iv) Find the value of such that P(T > B) = 0.01, where T = Σ₁₁Z₁² + 10₁ W₁². ẞ Σ{1Z2 Σi,

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2. (20 pts) Let X and Y be random variables of the continuous type having the joint p.d.f. 8 f(x,y) = xy, 0≤x≤1, x ≤ y ≤ 2x a) Draw a graph that illustrate the domain of the joint pdf. b) Find the marginal pdfs of X and Y. c) Compute x Hy d) Compute o2, and o. e) Calculate Cov(X, Y) and p.