fx, y(x, y) = = [c, if x² + y² ≤ 1, x ≥ 0, y ≥ 0; otherwise. Determine the following: 1. The value c and the marginal probability density functions for X and Y. 2. The conditional probability density function of X given Y = y, where 0 < y < 1. 3. Are X and Y independent? 4. The covariance Cov(X, Y) and correlation p(X, Y).
fx, y(x, y) = = [c, if x² + y² ≤ 1, x ≥ 0, y ≥ 0; otherwise. Determine the following: 1. The value c and the marginal probability density functions for X and Y. 2. The conditional probability density function of X given Y = y, where 0 < y < 1. 3. Are X and Y independent? 4. The covariance Cov(X, Y) and correlation p(X, Y).
fx, y(x, y) = = [c, if x² + y² ≤ 1, x ≥ 0, y ≥ 0; otherwise. Determine the following: 1. The value c and the marginal probability density functions for X and Y. 2. The conditional probability density function of X given Y = y, where 0 < y < 1. 3. Are X and Y independent? 4. The covariance Cov(X, Y) and correlation p(X, Y).
Let random variables X,Y have joint probability density function.
Transcribed Image Text:fx,y(x, y) =
0,
if x² + y² ≤ 1, x ≥ 0, y ≥ 0;
otherwise.
Determine the following:
1. The value c and the marginal probability density functions for X and Y.
2. The conditional probability density function of X given Y
3. Are X and Y independent?
4. The covariance Cov(X, Y) and correlation p(X, Y).
=
y, where 0 < y < 1.
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
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