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.
