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Thread: Constructing a p.m.f.

  1. #1
    Rhymes with Orange Chris L T521's Avatar
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    Constructing a p.m.f.

    I'm still having a bit of trouble trying to understand this stuff.

    Let a chip be taken at random from a bowl that contains six white chips, three red chips, and one blue chip. Let the random variable $\displaystyle X=1$ if the outcome is a white chip; let $\displaystyle X=5$ if the outcome is a red chip; and left $\displaystyle X=10$ if the outcome is a blue chip.

    (a) Find the p.m.f. of $\displaystyle X$
    [snip]
    Source: Probability and Statistical Inferences, 7E, by Hoggs and Tanis

    I understand that $\displaystyle P(X=1)=\frac{6}{10}$, $\displaystyle P(X=5)=\frac{3}{10}$, and $\displaystyle P(X=10)=\frac{1}{10}$.

    My issue here is determining a proper value for the numerator of my $\displaystyle f(x)=P(X=x)$. My stab at this would be to say that the p.m.f. has the form of $\displaystyle f(x)=\frac{u}{10}$, where $\displaystyle u$ is the part I can't figure out.

    I see a pattern though:

    $\displaystyle X=1:~~~~~6$

    $\displaystyle X=5:~~~~~3$

    $\displaystyle X=10:~~~~\!1$

    The difference between the first two terms is 3, and the last two terms is 2. Other than that, I'm at a standstill.

    I'd appreciate any input!

    --Chris



    w00t!!! my 9th post!!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Chris L T521 View Post
    I'm still having a bit of trouble trying to understand this stuff.

    Source: Probability and Statistical Inferences, 7E, by Hoggs and Tanis

    I understand that $\displaystyle P(X=1)=\frac{6}{10}$, $\displaystyle P(X=5)=\frac{3}{10}$, and $\displaystyle P(X=10)=\frac{1}{10}$.

    My issue here is determining a proper value for the numerator of my $\displaystyle f(x)=P(X=x)$. My stab at this would be to say that the p.m.f. has the form of $\displaystyle f(x)=\frac{u}{10}$, where $\displaystyle u$ is the part I can't figure out.

    I see a pattern though:

    $\displaystyle X=1:~~~~~6$

    $\displaystyle X=5:~~~~~3$

    $\displaystyle X=10:~~~~\!1$

    The difference between the first two terms is 3, and the last two terms is 2. Other than that, I'm at a standstill.

    I'd appreciate any input!

    --Chris



    w00t!!! my 9th post!!
    $\displaystyle
    f(x) = \begin{cases}
    \frac{6}{10}, &x\in \{1\},\\
    \frac{3}{10}, &x\in \{5\},\\
    \frac{1}{10}, &x\in \{10\},\\
    0, &x\in \mathbb{R}\backslash \{1,\ 5,\ 10\}.\end{cases}
    $

    RonL
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