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Math Help - Expectation

  1. #1
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    Question Expectation

    I am wondering if I could get help on the following HW problem:
    3 trails each have the same probability of success. If X is the total # of successes and if E[X]=1.8. What is the smallest possible value of P(X=3)?
    I know that the answer is 0 but I do not know why. I'll appreciate any help.
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  2. #2
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    Can you post the exact question?
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by thomas_donald View Post
    I am wondering if I could get help on the following HW problem:
    3 trails each have the same probability of success. If X is the total # of successes and if E[X]=1.8. What is the smallest possible value of P(X=3)?
    I know that the answer is 0 but I do not know why. I'll appreciate any help.
    Let p be the probability of success on a single trial. Then:

    E(X)=0.P(x=0)+1.P(x=1)+2.P(x=2)+3.P(x=3)=1.8\ \ \ \ ...(1)

    where:

    P(x=0)=(1-p)^3,

     <br />
P(x=1)=3.(1-p)^2.p<br />
,

     <br />
P(x=2)=3.(1-p).p^2<br />
,

     <br />
P(x=3)=p^3<br />
.

    Substituting these into the equation (1) gives a cubic in p and the question wants to know the smallest positive root of this cubic.

    CB
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  4. #4
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    Thanks a lot for the help.
    This is the exact question and the trails are not independent.
    I found the answer.
    Thanks again.
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