Question Video: Calculating the Expected Value from of a Discrete Random Variable Mathematics

The table shows the probability distribution of a fair six-sided die. Determine 𝐸(π‘₯).

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Video Transcript

The table shows the probability distribution of a fair six-sided die. Determine 𝐸 of π‘₯.

The top row of our table, labelled π‘₯, shows all the possible outcomes on the die, numbers one, two, three, four, five, and six. The bottom row shows the probability of π‘₯ equals π‘₯. The probability that we land on a one when rolling a fair six-sided die is one-sixth. Likewise, the probability of landing on a two, a three, a four, a five, or a six are all equal to one-sixth.

We’ve been asked to determine or calculate 𝐸 of π‘₯, which is the mean or the expected value. This expected value is calculated by working out the sum of π‘₯ multiplied by the probability that π‘₯ equals π‘₯. Firstly, we multiply one by one-sixth. Then we add two multiplied by one-sixth.

Continuing for the other values in our table gives us three multiplied by one-sixth, four multiplied by one-sixth, five multiplied by one-sixth, and finally six multiplied by one-sixth. We could type this calculation into the calculator in one go.

Alternatively, each of the individual multiplication sums give us one-sixth, one-third, one-half, two-thirds, five-sixths, and one. Finding the sum of these numbers gives us seven-halves, which is the same as 3.5. Therefore, the 𝐸 of π‘₯, the expected value or mean, is 3.5.

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