Determine if the following could be a probability distribution for a discrete random variable, X. If no, state why. X 20 30 40 5
0 P(X=x) 1.1 0.6 .2 .1 Yes, the probabilities are all positive. No, while the probabilities are all positive, the P(X=20)=1.1. Probabilities cannot exceed 1. No, the values of X are too far apart and the probabilities add up to a value greater than 1. Yes, the probabilities add to 1 and they are all positive.
We know that the probability p of a given event is 0 ≤ p ≤1. This means that given an event, its probability should be between zero and one.
In this problem we see that P(X=20) = 1.1 which is greater than one. Therefore, this cannot be a probability distribution given that this particular case exceeds the value of 1.
