Question

Find the value of the constant c so that each is a continuous joint density of two-dimensional random variable (X, Y). 1) fxy(x,y)=c, 6.5<=x<=8.5 and 100<=y<=200 2) fxy(x,y)=cxy, 6.5=

Answer 1

To find the value of the constant c for the joint density function fxy(x,y), we need to ensure that the total probability under the function is 1. We can calculate the value of c for both cases by setting up appropriate equations for the total probability.

Step-by-step explanation:

To find the value of the constant c for the joint density function fxy(x,y), we need to ensure that the total probability under the function is 1. For the first case, where fxy(x,y) = c, the function is constant over the given ranges of x and y. To find the value of c, we need to calculate the area of the rectangle defined by the ranges and set it equal to 1:

(8.5 - 6.5) * (200 - 100) * c = 1

For the second case, where fxy(x,y) = cxy, the function is proportional to x and y. To find the value of c, we need to calculate the double integral over the given ranges and set it equal to 1:

c * ∫100200 ∫6.58.5 xy dx dy = 1