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The function in a given table is a probability function of a discrete random variable π₯.
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Find the expected value of π₯.
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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.
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Here, thatβs the function of π₯.
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Before we can calculate the expected value of π₯, we first need to work out the value of the unknown in the table, π.
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Since π of π₯ is a probability function, we know the all outcomes sum to one.
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If we therefore subtract the given probabilities from one, weβll get the value of π.
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One minus 0.1 add 0.1 add 0.4 add 0.2 is 0.2.
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Our value of π is therefore 0.2.
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Now we can calculate the expected value of π₯.
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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.
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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.
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The expected value of π₯ is therefore 2.4.