Question Video: Probability Distribution Function of Discrete Random Variables Mathematics

Can the function in the table be a probability distribution function?

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Video Transcript

Can the function in the given table be a probability distribution function?

Now, what we have here certainly looks like it could be a probability distribution function. In the top row of the table, we have a countable set of values, which could be the range of a discrete random variable. And in the bottom row, we have some decimal values, which could be the associated probabilities. In order to check whether this could indeed represent a probability distribution function, we need to look at the probabilities more closely. And we should recall that the sum of all the probabilities in a probability distribution function must be equal to one.

Looking at the second row of the table and, in fact, looking just in the middle to values first of all, we can see that the sum of these values of 0.43 and 0.69 is a value greater than one. Of course, if we then sum all four values, we get an even larger value of 1.65. This means that this cannot be a probability distribution function, as if a discrete random variable could take each the values zero, one, four, and five with these associated probabilities would have a total probability greater than one, which is impossible. So, our answer is no.

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