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Thread: Expected value, variance and standard deviation

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    Expected value, variance and standard deviation

    Hi could someone help me with this question
    I already found that a) is 21/4 and c) is 297/48 but how do you find b) for Pr(X<m)

    Thanks
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    Re: Expected value, variance and standard deviation

    just find the pmf, and then discretely integrate this to determine the cdf

    Expected value, variance and standard deviation-clipboard01.jpg
    Last edited by romsek; Aug 31st 2017 at 06:00 PM.
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    Re: Expected value, variance and standard deviation

    I am only 12 and my teacher didn't tell me how to do that, could you please explain it a bit more simply
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    Re: Expected value, variance and standard deviation

    Quote Originally Posted by ChanelSapphire View Post
    I am only 12 and my teacher didn't tell me how to do that, could you please explain it a bit more simply
    Do you know what a probability mass function is?

    Can you list the set of possible events and determine for each what the value of $X$ is?

    Can you determine the probability of each of these events?
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    Re: Expected value, variance and standard deviation

    Quote Originally Posted by ChanelSapphire View Post
    Hi could someone help me with this question
    I already found that a) is 21/4 and c) is 297/48 but how do you find b) for Pr(X<m)
    Here is your sample space:
    $\{(h,1),~ (h,2),~(h,3),~(h,4),~(h,5),~(h,6),~(t,2),~(t,4),~( t,6),~(t,8),~(t,10),~(t,12)\}$
    $\mathscr{P}(X=1)=\dfrac{1}{12}$ WHY?
    $\mathscr{P}(X=2)=\dfrac{2}{12}$ WHY?

    Now YOU fill out this table.
    $\begin{array}{*{20}{c}}
    {\mathcal{P}(X = ?)}&|&{\_\_\_} \\
    \hline
    {\mathcal{P}(X = 1)}&|&{\_\_\_} \\
    {\mathcal{P}(X = 2)}&|&{\_\_\_} \\
    {\mathcal{P}(X = 3)}&|&{\_\_\_} \\
    {\mathcal{P}(X = 4)}&|&{\_\_\_} \\
    {\mathcal{P}(X = 5)}&|&{\_\_\_} \\
    {\mathcal{P}(X = 6)}&|&{\_\_\_} \\
    {\mathcal{P}(X = 8)}&|&{\_\_\_} \\
    {\mathcal{P}(X = 10)}&|&{\_\_\_} \\ {\mathcal{P}(X = 12)}&|&{\_\_\_} \\


    \end{array}$
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