Video: Finding the Expected Value of a Discrete Random Variable

The function in the given table is a probability function of a discrete random variable 𝑋. Find the expected value of 𝑋.

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Video Transcript

The function in a given table is a probability function of a discrete random variable π‘₯. Find the expected value of π‘₯.

For a discrete random variable, the expected value is worked out by finding the sum of the products of the value of the random variable and its probability. Here, that’s the function of π‘₯. Before we can calculate the expected value of π‘₯, we first need to work out the value of the unknown in the table, π‘Ž.

Since 𝑓 of π‘₯ is a probability function, we know the all outcomes sum to one. If we therefore subtract the given probabilities from one, we’ll get the value of π‘Ž. One minus 0.1 add 0.1 add 0.4 add 0.2 is 0.2. Our value of π‘Ž is therefore 0.2. Now we can calculate the expected value of π‘₯.

Each part of this is given by the product of the value of the random variable and its associated probability: zero multiplied by 0.1 add one multiplied by 0.2 add two multiplied by 0.1 add three multiplied by 0.4 add four multiplied by 0.2. Simplifying each parts of this sum gives us zero add 0.2 add 0.2 add 1.2 add 0.8, which gives us 2.4. The expected value of π‘₯ is therefore 2.4.

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