Question

(5) Ifpum.f of a dry. I'is P(x = x) =
for x = 0, 1, 2, 3, 4, 5 and = 0, othenvise
If a = P(X2) and b = P(X23), then E (X) =
(A) ab
(B) a>
her ab
(D) a -​

Answer 1

Step-by-step explanation:

For function, every element of the domain must have a unique image in co-domain...

(A)Let us redefine each function as a set of ordered pairs

and see if they satisfy the above condition (A) of a function f

1

={(1,2),(2,3),(3,4)} ; (4,5) cannot be an ordered pair as 5 does not belong to co-domain , Thus the element 4 of domain does not have an image.

f

2

={(1,4),(2,3),(2,4),(3,2)(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)}

The uniqueness is violated as the elements have not one but many images.

f

3

={(2,1),(3,2),(3,1),(4,1),(4,2),(4,3)} Not a function as in f

2

uniqueness is violated.

f

4

={(1,4),(2,3),(3,2)(4,1)} It is a function as each element has a unique image.