The outcome X of an experiment has only two possible values, X= 4 and X= 5. Given that the expected outcome E(X)= 4.2, find P(X= 5). Give yo

Question

The outcome X of an experiment has only two possible values, X= 4 and X= 5. Given that the expected outcome E(X)= 4.2, find P(X= 5). Give your answer as a decimal.

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Clara 2 months 2021-11-30T20:09:54+00:00 1 Answer 0 views 0

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    2021-11-30T20:11:00+00:00

    Answer:

    P(X=5) = 0.2

    Step-by-step explanation:

    Expected outcome, E(x) = ∑XP(X)

    ∑ = Summation

    X = outcomes

    P(X) = probability of an outcome

    E(X) = (4*P(X=4)) + (5*P(X=5)) = 4.2

    So, 4P(X=4) + 5P(X=5) = 4.2  … equation 1

    But the sum of probabilities = 1

    That is, P(X=4) + P(X=5) = 1 … equation 2

    Thus, we have the following system of equations

    4P(X=4) + 5P(X=5) = 4.2  … equation 1

    P(X=4) + P(X=5) = 1 … equation 2

    Multiply equation 2 by 4

    4*P(X=4) + 4*P(X=5) = 4*1

    4P(X=4) + 4P(X=5) = 4  … equation 3

    4P(X=4) + 5P(X=5) = 4.2  … equation 1

    4P(X=4) + 4P(X=5) = 4  … equation 3

    Subtract equation 3 from 1

    4P(X=4) – 4P(X=4)  + 5P(X=5) – 4P(X=5) = 4.2 – 4

    P(X=5) = 0.2

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