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Math Help - [SOLVED] Mean and Variance Question...

  1. #1
    Member looi76's Avatar
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    [SOLVED] Mean and Variance Question...

    Question:
    The random variable Y has the probability distribution given in the following table.

    Given that E(Y) = 4.9, show that a = b, and find the standard deviation of Y.


    Attempt:


    Need help continuing...
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  2. #2
    Senior Member Peritus's Avatar
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    <br />
\begin{gathered}<br />
  \sum\limits_i {y_i P(Y = y_i ) = 4.9 \Rightarrow 3.55 + 4a + 5b = 4.9}  \hfill \\<br />
  \sum\limits_i {P\left( {Y = y_i } \right) = 1 \Rightarrow 0.7 + a + b = 1}  \hfill \\ <br />
\end{gathered}

    2 equations in 2 unknowns...
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  3. #3
    Member looi76's Avatar
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    Quote Originally Posted by Peritus View Post
    <br />
\begin{gathered}<br />
  \sum\limits_i {y_i P(Y = y_i ) = 4.9 \Rightarrow 3.55 + 4a + 5b = 4.9}  \hfill \\<br />
  \sum\limits_i {P\left( {Y = y_i } \right) = 1 \Rightarrow 0.7 + a + b = 1}  \hfill \\ <br />
\end{gathered}

    2 equations in 2 unknowns...
    But in the textbook, the answer is a = b = 0.15
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  4. #4
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    If you plug in a = 0.15 and b = 0.15 into both equations Peritus provided, don't they both work out? Hence a = b = 0.15 is the solution.
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