Question

A given probability equation is P(x) = 2x-1/16 (where x can be 1,2,3 or 4) does this determine probability distribution why or why not

yes because The sum of all of the probabilities is not 1.

no because the sum of all of the probabilities is not 1.

no because the sum of all of the probabilities is 1.

yes because the sum of all of the probabilities is 1.

Answer 1

Yes, because the sum of all of the probabilities is 1.

Explanation:

The given probability equation is:

`P(x)=(2x-1)/(16)`, where x belongs to {1,2,3,4}.

`P(1)=(2(1)-1)/(16)=(1)/(16)`

`P(2)=(2(2)-1)/(16)=(3)/(16)`

`P(3)=(2(3)-1)/(16)=(5)/(16)`

`P(4)=(2(4)-1)/(16)=(7)/(16)`

Let us sum all the probabilities to obtain;

`P(1)+P(2)+P(3)+P(4)=(1)/(16)+ (3)/(16)+(5)/(16)+(7)/(16)`

`P(1)+P(2)+P(3)+P(4)=(1+3+5+7)/(16)`

`P(1)+P(2)+P(3)+P(4)=(16)/(16)`

`P(1)+P(2)+P(3)+P(4)=1`

Since the sum of all the probabilities is 1, it is a probability distribution