Question Video: Finding an Unknown given the Probability Distribution Function for a Discrete Random Variable | Nagwa Question Video: Finding an Unknown given the Probability Distribution Function for a Discrete Random Variable | Nagwa

# Question Video: Finding an Unknown given the Probability Distribution Function for a Discrete Random Variable Mathematics • Third Year of Secondary School

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The function in the given table is a probability distribution function of a discrete random variable π₯. Find the value of π.

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### Video Transcript

The function in the given table is a probability distribution function of a discrete random variable π₯. Find the value of π.

Remember, a discrete random variable can take on multiple different values, each with an associated probability, as long as those values are discrete. Now, the probability distribution function, here thatβs represented by a table, generates probabilities of value π of π₯, given some outcome of value π₯. And the following properties must hold.

First, the sum of ππ₯ must be equal to one. Second, any individual value of π of π₯, in other words any individual probability given in the table, must be greater than or equal to zero and less than or equal to one. So the property weβre going to apply in order to be able to answer this question is the first of these. Itβs the sum of ππ₯ must be equal to one.

The values of π of π₯ are given in the second row of our table. Since these must sum to one, we can say that one-fifth plus one-tenth plus three-tenths plus one-tenth plus π must be equal to one. Now, of course, one-fifth is equivalent to two-tenths. So the sum of each of these fractions is seven-tenths. And seven-tenths plus π is equal to one. To solve for π, weβll subtract seven-tenths from both sides, where one minus seven-tenths is equal to three-tenths. So π is equal to three-tenths.

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