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Mon 15 Oct, 2012 08:49 am
A bivariate, continuous random variable Z = (X,Y) has the following probability
density:
f(x, y) = A sin(x+y) for 0 ≤ x, y ≤ π and 0 otherwise.
a) Find the value of A that normalizes the distribution.
b) Find the mean value of Y, knowing that X = π/2.
c) Find the mean value of X.
d) Find the covariance of X and Y.
@angelrocksvid,
Are you sure this is correct? Your pdf is negative when:
pi < x+y < 2*pi
@markr,
that will be equal to 0... see otherwise case
@angelrocksvid,
No, this:
0 ≤ x, y ≤ π
means BOTH x AND y can be in the range 0 to π
This:
0 ≤ x + y ≤ π
means the SUM of x AND y is in the range 0 to π
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