which is a valid probability function

a) p(x) for x=0,1,2
b)p(x)=x/1 for 0,1,2
c) p(x)=x/2 for 0,1,2

In order for a function to be a valid probability function, it must satisfy certain criteria. The criteria are as follows:

1. The probability values should be non-negative: All probability values should be greater than or equal to zero.

2. The sum of all probability values should be equal to 1: When you add up all the probability values for all possible outcomes, the total probability should equal 1.

Now let's analyze the probability functions provided:

a) p(x) for x=0,1,2

In this case, you need to verify if all the probability values are non-negative and if their sum equals 1.

b) p(x) = x/1 for 0,1,2

Here, you need to check if all the probability values are non-negative and if their sum equals 1.

c) p(x) = x/2 for 0,1,2

Similarly, you need to ensure that all the probability values are non-negative and if their sum adds up to 1.

To verify each function's validity, let's calculate the probabilities for each possible outcome:

a) p(0) = ?, p(1) = ?, p(2) = ?

b) p(0) = ?, p(1) = ?, p(2) = ?

c) p(0) = ?, p(1) = ?, p(2) = ?

Once we calculate these values, we can determine if the sum of the probabilities is equal to 1 and if all the probabilities are non-negative.