Question

Let random variables X and Y have the joint pmf : f(x,y)=

ci+y ,x={2,3},y={1,2,3}
find the value of c

Answer 1

To find the value of c in the joint pmf f(x,y) = ci+y, x={2,3}, y={1,2,3}, we need to set the sum of the probabilities equal to 1 and solve for c.

Step-by-step explanation:

To find the value of c, we need to use the fact that the joint probability mass function (pmf) must sum to 1. We can write out the given joint pmf for each value of X and Y:

• f(2,1) = c + 1
• f(2,2) = c + 2
• f(2,3) = c + 3
• f(3,1) = c + 1
• f(3,2) = c + 2
• f(3,3) = c + 3

We can sum these probabilities and set the result equal to 1 to solve for c:

(c + 1) + (c + 2) + (c + 3) + (c + 1) + (c + 2) + (c + 3) = 1

6c + 12 = 1

6c = -11

c = -11/6

Therefore, the value of c is -11/6 or approximately -1.83.