Problem #2 Consider the discrete joint density defined in the table at right. The entries in the table correspond to fxy(x, y). A. What is the marginal distribution of X? B. What is the marginal distribution of Y? C. What is E[X]? E[Y]? E[XY]? D. What is Cov(X, Y)? E. Are X and Y independent? Explain/justify your answer. y = 0 y = 1 x = 2 0.2 0.5 x = 3 0.2 0.1

Problem #2 Consider the discrete joint density defined in the table at right. The entries in the table correspond to fxy(x, y). A. What is the marginal distribution of X? B. What is the marginal distribution of Y? C. What is E[X]? E[Y]? E[XY]? D. What is Cov(X, Y)? E. Are X and Y independent? Explain/justify your answer. y = 0 y = 1 x = 2 0.2 0.5 x = 3 0.2 0.1

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter1: Functions

Section1.2: Functions Given By Tables

Problem 11E: A Troublesome Snowball One winter afternoon, unbeknownst to his mom, a child bring a snowball into...

See similar textbooks

Similar questions

A Troublesome Snowball One winter afternoon, unbeknownst to his mom, a child bring a snowball into the house, lays it on the floor, and then goes to watch T.V. Let W=W(t) be the volume of dirty water that has soaked into the carpet t minutes after the snowball was deposited on the floor. Explain in practical terms what the limiting value of W represents, and tell what has happened physically when this limiting value is reached.
1.) Suppose X and Y have joint density function f(x,y)= 8xy/3 on x is greater than or equal to 0 and less than or equal to 1. and y is greater than x and is less than or equal to 2x. a.) Find P( Y< 0.8) b.) Find the marginal density function of X c.) What is E(X)?
5. Suppose that the joint probability density function of X and Y is given by f(x, y) = C (x² + y), 0 < x < 2, 0 < y < 2 and f(x, y) = 0 otherwise. (a) Find C. (b) Find the marginal density functions of X and Y. (c) Compute P(X > Y). (d) Compute E[X]. (e) Compute E[Y].
Suppose that the joint probability density function of X and Y is fX,Y(x,y) = 10.125(x2 – y2) e−3x , for 0<x<∞ and -x<y<x 0, otherwise Give your answers to the below questions in two decimal places where appropriate. (a) The marginal probability density function of X is given by: fX(x) = A xB e-3x , for 0<x<∞ 0, otherwise Find the value of A. (b) Find the value of B. (c) The conditional probability density function of Y, given that X=x for some x>0, takes the following form: fY|X=x(y) = C (x2-y2) xD e-Ex, for -x<y<x 0, otherwise. Find the value of C (d)Find the value of D. (e)Find the value of E.
For a certain psychiatric clinic suppose that the random variable X represents the total time (in minutes) that a typical patient spends in this clinic during a typical visit (where this total time is the sum of the waiting time and the treatment time), and that the random variable Y represents the waiting time (in minutes) that a typical patient spends in the waiting room before starting treatment with a psychiatrist. Further, suppose that X and Y can be assumed to follow the bivariate density function fXY(x,y)=λ2e−λx, 0<y<x, where λ > 0 is a known parameter value. (a) Find the marginal density fX(x) for the total amount of time spent at the clinic. (b) Find the conditional density for waiting time, given the total time. (c) Find P (Y > 20 | X = x), the probability a patient waits more than 20 minutes if their total clinic visit is x minutes. (Hint: you will need to consider two cases, if x < 20 and if x ≥ 20.)
1 How can I find the distribution and density in closed form of the severity model of losses for the sum of n-losses when α = 0.5 and β = 1 (Levy)? Could someone explain to me how to calculate closed forms in general because I do not understand the concept? X_i(t) ∼ S_α(β, γ, δ; 0)
Suppose X and Y have a joint density function of f(x,y)=6x2y, 0<x<1, 0<y<1. Find P(X+2Y<1).
1. Let f (x) = cx 3 and S X = [0, 2] (X is continuous and c is a constant). a. What value of c will make f (x) a valid density?b. What is P (X = 1)?c. What is P (X = 1 or X = 2)?
Xavier and Yolanda both have classes that end at noon and they agree to meet every day after class. They arrive at the coffee shop independently. Xavier's arrival time is X and Yolanda's arrival time is Y, where X and Y are measured in minutes after noon. The individual density functions are given.(Xavier arrives sometime after noon and is more likely to arrive promptly than late. Yolanda always arrives by 12:10 PM and is more likely to arrive late than promptly.) After Yolanda arrives, she'll wait for up to 45 minutes for Xavier, but he won't wait for her. Find the probability that they meet. (Round your answer to three decimal places.)
The Weibull distribution has the following density functionf(x) = (α / βα)*xα-1*e-(x/β)^α, y ≥ 0 (Shown in picture) 1. Find the cumulative distribution function and express the median as a function of the parameters α and β.2. Under what condition will this density function equal the exponential density function?3. What would be the expression for the joint distribution of 10 independent random variables with the Weibull density function? Summarize it as much as possible.
(1) Find P(X > 2.54 and Y > 1) (2) Find the marginal probability density function fx(2), and hence fx(4.31)(3) Find the marginal probability density function fy (y) and hence find fy(1.43)
Suppose f(x)=3x2, 0<x<1 is a density function of X. Find P(1/2<X<2).