In: Statistics and Probability
Let (X, Y) be a random vector with a function of the joint density given by ˜ fX, Y (x, y) = k (2x + y) I (2,6) (x) I (0.5) (y)
a) Determine k so that f X, Y (x, y) is a true probability density function joint quality.
b) Determine the marginal probability density functions of X and Y.
c) Calculate P (3 <X <4, Y> 2).
d) Calculate P (X + Y> 4).
please note that I(0.5) is improper representation for defining range, so assuming the correction to be as I(0,5) the question has been solved.
Thanks!