More p.m.f [p.d.f.] questions!

**Chris L T521** · September 24th 2008, 09:35 AM

I think I have the hang of this now, but I have a minor question:

I am to find the constant $c$ which would make $f(x)$ satisfy all the conditions of being a p.m.f.

$f(x)=c(1/4)^x;~~~x=1,2,3,...$

I assumed that this would continue on to infinity [for there was another similar to this, where it explicitly said that $x=1,2,3...n$ ]

So, I figured that $f(x)>0$ ;

I also noticed that $\sum_{x\in S}f(x)=1\implies \sum_{x=1}^{\infty}c(1/4)^x=1$ . The series is geometric, where $a=c$ , and $r=\frac{1}{4}$ . Thus, it converges to $\frac{c}{1-\frac{1}{4}}=\frac{c}{\frac{3}{4}}=\frac{4}{3}c$

So for $\frac{4}{3}c=1,~c=\frac{3}{4}$

However, my text tells me that the answer is 3.

Maybe I'm overlooking one simple thing...wait!

How do I apply the last property of a p.m.f:

$P(X\in A)=\sum_{x\in A}f(x)~~~\text{where}~A\subset S$

to this problem?

I'd appreciate any input!

--Chris

**Plato** · September 24th 2008, 09:51 AM

$\sum\limits_{k = 1}^\infty {\left( {1/4} \right)^k } = \frac{{(1/4)}}<br /> {{1 - (1/4)}} = \frac{1} {3}\quad \Rightarrow \quad c = 3$

**Moo** · September 24th 2008, 10:49 AM

Yo Chris...

Remember it's ${\color{red}1}+r+r^2+\dots+r^n+\dots$ that equals $\frac{1}{1-r}$

If it starts at $r$ (which is the case here since the sum starts at 1), we have : $r+r^2+\dots+r^n+\dots=r \left(1+r+r^2+\dots+r^n+\dots\right)={\color{red}r } \cdot \frac{1}{1-r}$

Go back to high school !

**Chris L T521** · September 24th 2008, 01:11 PM

Originally Posted by Moo

Yo Chris...

Remember it's ${\color{red}1}+r+r^2+\dots+r^n+\dots$ that equals $\frac{1}{1-r}$

If it starts at $r$ (which is the case here since the sum starts at 1), we have : $r+r^2+\dots+r^n+\dots=r \left(1+r+r^2+\dots+r^n+\dots\right)={\color{red}r } \cdot \frac{1}{1-r}$

Ahaha...I can't believe I didn't see that...

Go back to high school !

Never!!

--Chris

Thread: More p.m.f [p.d.f.] questions!

LinkBack

Thread Tools

Display

More p.m.f [p.d.f.] questions!

Similar Math Help Forum Discussions

More log questions

Please someone help me with just 2 questions?

Some Questions !

Plz solve these questions.(Trignometry statement questions)

Assorted algebraic questions ( Read this before asking some questions! )

Search Tags