1. Let $(x) = 2x2 and let Y = $(x). (a) Consider the case X ~U(-1,1)....

Question

Question

1. Let $(x) = 2x2 and let Y = $(x). (a) Consider the case X ~U(-1,1). Obtain fy and compute E[Y] (b) Now instead assume that

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

Y(x) Se PDF e X is giuem by 1 - thesusise 0therusize kmltie dindu bullenunen (e D F ) of xis guurn b Y(-1) Fx () PLX : 1

Fyly) ny0 P (- ) Fx xE-VE4) A, Fly)Fx(J5y) - Fx (- ) S dlfnentiading as (t()- 0 otharure ( 0 otherwize नु huwin HenceEY dy OR, vk.4 c(clue de euen unlion) 3 ao, E(YE , POF GYisPyly 0tharusise 04 therusine Xis a kentinugus nandem vaua bl

therwis and usheneue 0Yp Jn all other Os iyly) o and in had one A0, is pnible de chwene fx auch that

Add a comment

Answer 2

Similar Homework Help Questions

Let $(x) = 2x2 and let Y = $(X). assume that Y ~ U(0,1/2) and that X is a continuous random variable. fx(x) = 0 whe...

Let $(x) = 2x2 and let Y = $(X). assume that Y ~ U(0,1/2) and that X is a continuous random variable. fx(x) = 0 whenever |2| > 1. Obtain an expression linking fx(x) to fx(-x) for xe (-1,1). Show that E[X] = -2/3 + 28. xfx(x) dx. Using your expression linking fx(x) and fx(-x), obtain an upper bound for E[X] and a pdf fx for which this bound is attained. [10]
3. Let X.. U(-1,1) for i € {1, 2, 3). (a) Write down the expected value...

3. Let X.. U(-1,1) for i € {1, 2, 3). (a) Write down the expected value and variance of X,. Sketch the pdf fx. [3] (b) Let Y = X1 + X2. Compute the pdf fy of Y and sketch it. Using fy, or otherwise, compute the expected value and variance of Y. (7) (c) Let Z = X1 + X2 + X3 = Y + X3. Using exactly the same technique that you used in part (b), it can...
Let U ~uniform(0,1). Let Y =−ln(1−U). hint: If FX (x) = FY (y) and supports x,y...

Let U ~uniform(0,1). Let Y =−ln(1−U). hint: If FX (x) = FY (y) and supports x,y ∈ D, X and Y have the same distribution. Find FY (y) and fY (y). Now, it should be straight forward that Y follows distribution with parameter_____________-

- Let X, 1.2.4. U(-1,1) for i € {1, 2, 3). (a) Write down the expected...

- Let X, 1.2.4. U(-1,1) for i € {1, 2, 3). (a) Write down the expected value and variance of X]. Sketch the pdf fxı. [3] (b) Let Y = X1 + X2. Compute the pdf fy of Y and sketch it. Using fy, or otherwise, compute the expected value and variance of Y. (7) (c) Let Z = X1 + X2 + X3 = Y + X3. Using exactly the same technique that you used in part (b), it...
1. Let X and Y be two jointly continuous random variables with joint CDF otherwsie a....

1. Let X and Y be two jointly continuous random variables with joint CDF otherwsie a. Find the joint pdf fxy(x, y), marginal pdf (fx(x) and fy()) and cdf (Fx(x) and Fy)) b. Find the conditional pdf fxiy Cr ly c. Find the probability P(X < Y = y) d. Are X and Y independent?
5. Let X have a uniform distribution on the interval (0,1). Given X = x, let...

5. Let X have a uniform distribution on the interval (0,1). Given X = x, let Y have a uniform distribution on (0, 2). (a) The conditional pdf of Y, given that X = x, is fyıx(ylx) = 1 for 0 < y < x, since Y|X ~U(0, X). Show that the mean of this (conditional) distribution is E(Y|X) = , and hence, show that Ex{E(Y|X)} = i. (Hint: what is the mean of ?) (b) Noting that fr\x(y|x) =...

Let U U (0,1) and let Y=1-U. Derive an expression for the odf Fy() of Y...

Let U U (0,1) and let Y=1-U. Derive an expression for the odf Fy() of Y in terms of the odf of U and hence show that Y U (0,1).
Let X, Y be jointly continuous with joint density function (pdf) fx,y(x, y) *(1+xy) 05 x...

Let X, Y be jointly continuous with joint density function (pdf) fx,y(x, y) *(1+xy) 05 x <1,0 <2 0 otherwise (a) Find the marginal density functions (pdf) fx and fy. (b) Are X and Y independent? Why or why not?
2. Suppose X and Y are independent continuous random variables. Show that P(Y < X) =...

2. Suppose X and Y are independent continuous random variables. Show that P(Y < X) = | Fy(x) · fx (x) dx -oo where Fy is the CDF of Y and fx is the PDF of X [hint: P[Y E A] = S.P(Y E A|X = x) · fx(x) dx]. Rewrite the above equation as an expectation of a function of X, i.e. P(Y < X) = Ex[•]. Use the above relation to compute P[Y < X] if X~Exp (2)...

7.4 Let X ~ U(-1,1) and Y = x2. a. What are the density, the distribution...

7.4 Let X ~ U(-1,1) and Y = x2. a. What are the density, the distribution function, the mean, and the variance of Y: b. What is Pr[Y < 0.5]? 7.5 Let X – U(0,1), and let Y = eax for some a > 0. What are the density, the distribution function, the mean, and the variance of Y?

1. Let $(x) = 2x2 and let Y = $(x). (a) Consider the case X ~U(-1,1)....

Homework Answers

Add Answer to:
1. Let $(x) = 2x2 and let Y = $(x). (a) Consider the case X ~U(-1,1)....

Post as a guest

Earn Coins

Let $(x) = 2x2 and let Y = $(X). assume that Y ~ U(0,1/2) and that X is a continuous random variable. fx(x) = 0 whe...

3. Let X.. U(-1,1) for i € {1, 2, 3). (a) Write down the expected value...

Let U ~uniform(0,1). Let Y =−ln(1−U). hint: If FX (x) = FY (y) and supports x,y...

- Let X, 1.2.4. U(-1,1) for i € {1, 2, 3). (a) Write down the expected...

1. Let X and Y be two jointly continuous random variables with joint CDF otherwsie a....

5. Let X have a uniform distribution on the interval (0,1). Given X = x, let...

Let U U (0,1) and let Y=1-U. Derive an expression for the odf Fy() of Y...

Let X, Y be jointly continuous with joint density function (pdf) fx,y(x, y) *(1+xy) 05 x...

2. Suppose X and Y are independent continuous random variables. Show that P(Y < X) =...

7.4 Let X ~ U(-1,1) and Y = x2. a. What are the density, the distribution...

1. Let $(x) = 2x2 and let Y = $(x). (a) Consider the case X ~U(-1,1)....

Homework Answers

Add Answer to: 1. Let $(x) = 2x2 and let Y = $(x). (a) Consider the case X ~U(-1,1)....

Post as a guest

Earn Coins

Add Answer to:
1. Let $(x) = 2x2 and let Y = $(x). (a) Consider the case X ~U(-1,1)....