1. 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!!

2. Originally Posted by Chris L T521
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