Is the following distribution a probability distribution
(x, P(X)) = (-2,1.23); (-1, 0.15) ; (0, -1.20); (1, 0.52); (2, 0.30)
There are five ordered pairs: X values and their probabilities for example P(1) = 0.52.
X, -2, -1, 0, 1, 2
P(X), 1.23, 0.15, -1.20, 0.52, 0.30
True or False?
there are 5 pairs, but they are not all probabilities. Why not?
False.
In order for a distribution to be a probability distribution, the probabilities must satisfy certain conditions:
1. Each probability must be non-negative.
2. The sum of all probabilities must be equal to 1.
In the given distribution, the probability for the X value 0 is -1.20, which violates the first condition of being non-negative. Therefore, the given distribution is not a probability distribution.
To determine if the given distribution is a probability distribution, we need to check if all the probabilities are non-negative and their sum is equal to 1.
Let's calculate the sum of the probabilities:
Sum = 1.23 + 0.15 + (-1.2) + 0.52 + 0.30
Sum = 1.7 + (-1.2) + 0.82
Sum = 1.7 - 1.2 + 0.82
Sum = 0.5 + 0.82
Sum = 1.32
Since the sum of the probabilities is not 1, this distribution is not a probability distribution.
Therefore, the statement "False" is correct.