Determine whether or not the distribution is a probability distribution and select the reason(s) why or why not. X 0 1 2 P(X) 0 1/3 2/3 Select all that apply: The given distribution is a probability distribution, since the probabilities lie inclusively between 0 and 1. The given distribution is not a probability distribution, since at least one of the probabilities is greater than 1 or less than 0. The given distribution is a probability distribution, since the sum of probabilities is equal to 1. The given distribution is not a probability distribution, since the sum of probabilities is not equal to 1.

The given distribution is a probability distribution, since the probabilities lie inclusively between 0 and 1.
The given distribution is a probability distribution, since the sum of probabilities is equal to 1.

The probability distribution is given as:

X 0 1 2

P(X) 0 1/3 2/3

From the above table of probability distribution, we can see that each probability value is between 0 and 1 (inclusive)

Also, the sum of probabilities is 1

i.e. 0 + 1/3 + 2/3 = 1

Hence, the distribution is a probability distribution, and the reasons are

The given distribution is a probability distribution, since the probabilities lie inclusively between 0 and 1.
The given distribution is a probability distribution, since the sum of probabilities is equal to 1.

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