2. Let X,,X, id F(x), where f(x) = e.0

Here the given p.d.f is of chi-square distribution with k= 2. As we know that, If X~ chi-square…

Answered: 2. Let X, X, F(x), where f(x) = {e.0

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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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5. Let f(x, y) = P(X =x,Y = y), X = 2,3,4, Y = 1,2,3,4, where P is given by the table below: X = 2 X = 3 X = 4 Y = 1 Y = 2 Y = 3 1/20 2/20 1/20 2/20 1/20 3/20 1/20 2/20 2/20 2/20 1/20 Y = 4 2/20 For problems (a) - (d) below write your work using the correct notation in terms of f (e.g. f(x, y), fy: f,(3), fyp fxp(4) ): (a) Verify that f is a joint probability mass function. (b) Find the marginal distribution for each random variable. Are both random variables independent? (c) Find the mean and variance of each marginal distribution. (d) Find the conditional probability function of Y given X =3. (e) Find E(Y|X = 3) and V(Y|X = 3). (f) Find P(X+Y =5), P(Y >1), and P(X +Y =5|Y > 1).
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3. A continuous function f is defined on the closed interval -4≤x≤4. The graph of the function, shown in the figure to the right consists of a line and two curves. There is a value a, -4≤a<4, for which the Mean Value Theorem, applied to the interval [a,4] guarantees a value c, a ≤ c <4 at which f'(c)=3. What are possible values of a? I. -4 II. 0 III. 2 A. I only B. II only D. II and III only E. I, II and III C. III only co (-4,-12) -2 4 12 10 8 6 4 2 -2 -4 -6 -8 -10 -12 1 (2,6) 2 3 (4.12)
5. If f(x, y) = = Find (1 0≤x≤ 1, 0≤ y ≤ 1 0 otherwise a. P(X > ¹/₂ |Y y|Y > ¹/2)
4.08 Consider Y with pmf p(y) = exp(-3.8)(3.8)'-2/(y-2)! defined on some set. ( a Determine a valid set. ( b Calculate P(Y > 3).
Find the difference of upper limit of 4th class interval and lower limit of 2nd class interval
Use the rules of expectations to show that Var(X) E(X-E(X))") E(X)- E(X) and Var(X + Y) = Var(X) + Var(Y) +2Cov(x,Y)
Please all the question
Find f, and f, and evaluate each at the given point. f(x, y) = e*y?, (In 9, 2) f,(x, y) = 1,x, v) = f,(In 9, 2) = f,(In 9, 2) =
Show that the functions(a) f(x)=1/(1+x2),x∈R, (b) g(x)=x/(1+x2),x∈R, are uniformly continuous, while the functions(c) f(x)=x2,x∈R, (d) g(x)=√∣x∣,x∈R, are not Through graph

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