Question

Random variables X and Y have the joint PMF with a constant k P(x,y)={kxy,0,​x=1,4;y=1,3 otherwise ​ Find the k, the constant .

Answer 1

To find the value of the constant k in the joint PMF, we set up and solve an equation that represents the sum of all the probabilities in the joint PMF equaling 1. The value of the constant k is 1/24.

Step-by-step explanation:

To find the value of the constant k in the joint PMF, we need to set up and solve an equation that represents the fact that the sum of all the probabilities in the joint PMF equals 1. Since the joint PMF is given by P(x,y) = kxy for x = 1,4 and y = 1,3, we can set up the equation:

k(1)(1) + k(1)(3) + k(4)(1) + k(4)(3) = 1

Simplifying and combining like terms gives:

5k + 3k + 4k + 12k = 1

24k = 1

k = 1/24

Therefore, the value of the constant k is 1/24.