Determine if the following are probability distributions (if no, state why).
a. X 3 6 9 12 15
P(X) 4/9 2/9 1/9 1/9 1/9
If you are talking "P(X)", isn't that probability?
To determine if the given values form a probability distribution, we need to check if the probabilities sum up to 1 and if all the probabilities are non-negative.
In this case, we have the following values:
X: 3 6 9 12 15
P(X): 4/9 2/9 1/9 1/9 1/9
To confirm if this is a probability distribution, let's check if the probabilities sum up to 1:
4/9 + 2/9 + 1/9 + 1/9 + 1/9 = 9/9 = 1
The sum of the probabilities is equal to 1, which is one of the conditions for a probability distribution.
Now, let's check if all the probabilities are non-negative. In this case, all the probabilities (4/9, 2/9, 1/9, 1/9, 1/9) are greater than or equal to zero, so this condition is also satisfied.
Therefore, the given values (X: 3 6 9 12 15 and P(X): 4/9 2/9 1/9 1/9 1/9) form a probability distribution since the probabilities sum up to 1 and all the probabilities are non-negative.