Question

?(?,?) = ?+?+? / ?? ??? ? = ?,?,?,?; ? = ?,?,?

where “c” is the last digit of your student ID a) Is it a continuous or discrete function? b) Can it be a probability distribution function? Explain. c) For what value or values of “c” this function can be a probability distribution function? d) Using a proper value of “c” (that makes the function a probability distribution function) find marginal distribution function g(x) if your student ID is an even number or marginal distribution function h(y) if your student ID is an odd number. (don’t do both)

MY ID:13201017 SO C=7

Answer 1

a) This is a discrete function

b) Let's put value of c as 7

x\y	0	1	2	Total
0	7/42	8/42	9/42	24/42
1	8/42	9/42	10/42	27/42
2	9/42	10/42	11/42	30/42
3	10/42	11/42	12/42	33/42
Total	34/42	38/42	42/42	114/42

To be a valid probability distribution, the grand total value should be 1 which in this case is 114/42. So, this is not a probability distribution

c)

(30 + 12c) / 42 = 1

or, 30 + 12c = 42

or, 12c = 12

or, c = 1

d) We need to find h(y), because student id is odd number.

h(0) = (6 + 4c) / 42 = (6 + 4 * 1) / 42 = 10/42

h(1) = (10 + 4c) / 42 = (10 + 4 * 1) / 42 = 14/42

h(2) = (14 + 4c) / 42 = (14 + 4 * 1) / 42 = 18/42