The document discusses a joint probability density function f(x1, x2) = x1 + x2 defined over the interval [0,1]. It is shown that the marginal densities are f(x1) = x1 + 1/2 and f(x2) = x2 + 1/2. Since the joint density does not equal the product of the marginal densities, X1 and X2 are not independent random variables. The conditional density of X1 given X2 = 0.5 is also calculated to be 1.

1. Let X1, and X2have joint density function given by:
f(x1, x2) = x1+ x2 0
Solution
a) marginal density function of X1= integral f(X1,X2)dX2 limits from 0 to 1
=X1+1/2
similarly marginal density function for X2= X2+1/2
b)X1 and X2 are not independent since f(X1)xf(X2)!=f(X1,X2)
c)conditional density function of X1 given (X2=0.5) = integral f(X1|X2=0.5) limits from 0 to 1
=1/2+1/2=1
d)http://en.wikipedia.org/wiki/Correlation_and_dependence open this link and you will find the
answer