00:01
Hello student, let x and y are discrete random variable with joint pmf t into 2 raised to x plus y by x factorial into y factorial for x is equal to 0, 1, 2, 3 and y is equal to 0, 1, 2, 3.
00:13
Now in a part of the question in order to find the constant c, let's equate the joint pmf to 1 that is t into summation of x 2 raised to x by x factorial to summation of y 2 raised to y by y factorial is equal to 1.
00:33
Therefore, c into t square into t square is equal to 1.
00:37
Therefore, c is equal to 1 by t raised to 4.
00:45
Now in b part of the question, we want to find the marginal pmf of x and y.
00:54
Marginal pmf of x is given by t x of x is equal to summation of y is equal to 0 to infinity, c into 2 raised to x by x factorial 2 raised to y by y factorial is c into 2 raised to x by x factorial taking outside summation y 2 raised to y by y factorial which is equal to c into 2 raised to x by x factorial into e square.
01:28
Substituting the value of c that is 1 by e raised to 4, 2 raised to x by x factorial into 2 raised to 2.
01:45
Then e square and e raised to 4 gets simplified that is marginal pmf of x is 1 by e square 2 raised to x by x factorial...