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The function in the given table is a probability function of a discrete random variable 𝑋.
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Find the value of 𝑎.
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So we’ve been given a table containing the possible values of 𝑥 and their given probabilities.
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Now in order to find 𝑎, we just need to use the fact that the sum of all probabilities has to equal one.
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So in order to find 𝑎, we simply take all our probabilities, add them together, and put them equal to one.
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This gives us two 𝑎 plus 0.3 plus 0.3 plus 𝑎 plus 𝑎 is equal to one.
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And now this can be simplified to four 𝑎 plus 0.6 equals one.
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Now we subtract 0.6 from either side.
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And this leaves us with four 𝑎 is equal to 0.4.
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And finally, we divide both sides by four.
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This gives us a final answer of 𝑎 is equal to 0.1.