Question

If the joint density function of X and Y is

f(x,y)=c(x^2−y^2)e^(−2x),

with 0≤x<∞and −x≤y≤x find each of the following.

(a) The conditional probability density of X, given Y=y>0.
Conditional density fX|Y(x,y)=
(Enter your answer as a function of x, with y as a parameter.)

(1 point) Applicants for the University of Statland take two tests, one for writing ability and the other on critical thinking, and normalised scores are recorded on each between 0 and 1. For a given applicant, let X be the score on the writing test and Y the score on the critical thinking test. A model for the joint probability density function for the two test scores can be taken as: (2z + y) for 0 < z < 1,0 < y < 2 0 elsewhere.

b. Find the marginal density of the critical thinking test score, and evaluate it at the point Y=1/3 ​​

Answer 1

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