1) Suppose that X and Y has joint density function [x+y 0 0 Based on the density function, a) calculate the probability, P(x² + y² ≤1) b) calculate the probability, P(Y>5X)
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- A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.Suppose X and Y have joint density f(x, y) = x + y 0 < x < 1,0 < y < 1. What is E(XY2)Q1) Discrete joint variables X and Y with probability density f(x,y) (pdf) are given in this table. Find: 1) The Covariance Cov(X,Y)? (Cov(X,Y) = MxY-MxMY) 2) The correlation (pxy) between X and Y where Pxy = Cov(X,Y) PXPY Y 3 fx(x) f(x,y) 1 2 1 1/4 1/4 0 X 2 0 1/4 1/4 fy(y) Note that 2 n=2 n=3 Px² = Σn²±²x² f(x, y) - μ and py² = Σ3y² f(x, y) – µ Zk=0
- 9. If X, Y have some bivariate density, prove that Var(X – Y) = Var(X)+Var(Y) – 2Cov(X,Y).7.Find the value of k if f (x, y) = k(1- x)(1- y) for0 < x, y < 1 is to be joint density function.Suppose that X and Y have a joint density function given by e-(a+y)r,y> 0, otherwise f(x, y) (a) Compute P(X < Y) (b) What is P(X = Y < 2X)?
- 5) For the following density function f(x) = c x2 (1–x), 0If f(x) is density function then f(x)<0. صوابSuppose fz(z) is a function given by So(23 – 2) if -z<0 | fz(2) = otherwise for a fixed constant c. Can fz(z) be a density function? Explain.The joint density function for X and Y is ху 0 < x < 2 and 0If and Y have the joint density function 2e-(*+y), 0The joint density function of X and Y is given by 0SEE MORE QUESTIONSRecommended textbooks for youFunctions and Change: A Modeling Approach to Coll…AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningFunctions and Change: A Modeling Approach to Coll…AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning