N: P(N=n)=(3/5)[(2/5)^n], find E(N)

**tcRom** · November 15th 2012, 03:32 PM

Suppose the number of children N of a random family satifies P(N=n)=(3/5)[(2/5)^n] where n=0,1,2,... Compute E(N).

I went through the math and I come up with 1, which is the probability space. So, I know I'm not going about this the right way.

$E(N=n)=\frac{3}{5}(\frac{2}{5})^0 + \frac{3}{5}(\frac{2}{5})^1 + \frac{3}{5}(\frac{2}{5})^2 + ...$

$=\sum_{n=0}^{\infty}\frac{3}{5}(\frac{2}{5})^n$

$=\frac{3}{5}\sum_{n=0}^{\infty}(\frac{2}{5})^n$

$=\frac{3}{5}\frac{5}{3}$

$=1$

Could somone point out the basic understanding of expected value that I seem to be missing in this problem?

**MacstersUndead** · November 15th 2012, 03:50 PM

I'm going to assume you mean expected value. Here is the definition

$\operatorname{E}[N] = n_1p_1 + n_2p_2 + \dotsb + n_kp_k \;.$

What you have is the sum of all possible probabilities, which of course must be equal to 1!
However, each of your probabilities P[N=i] has a weight n_i

**tcRom** · November 15th 2012, 03:59 PM

$E(N=n)=0*\frac{3}{5}(\frac{2}{5})^0 + 1*\frac{3}{5}(\frac{2}{5})^1 + 2*\frac{3}{5}(\frac{2}{5})^2 + ...$

$=\sum_{n=0}^{\infty}n*\frac{3}{5}(\frac{2}{5})^n$

$=\frac{2}{3}$

At least I was right about missing a basic understanding. The unfortunate part is that I need to learn how to go from the summation to the answer using paper and pencil, I won't always have access to a calculator that can do the sum for me...

**MacstersUndead** · November 15th 2012, 04:14 PM

I'm trying to remember back in my statistics class. If you were to take the natural log of both sides, would that help? when I see the product of n and (2/5)^n, that's what I want to do. EDIT:// but it is a sum still so it might not.

Thread: N: P(N=n)=(3/5)[(2/5)^n], find E(N)

LinkBack

Thread Tools

Display

N: P(N=n)=(3/5)[(2/5)^n], find E(N)

Re: N: P(N=n)=(3/5)[(2/5)^n], find E(N)

Re: N: P(N=n)=(3/5)[(2/5)^n], find E(N)

Re: N: P(N=n)=(3/5)[(2/5)^n], find E(N)

Similar Math Help Forum Discussions

Find an Equation of the Tangent Line to the parabola at the given point and find....

Given 3 points, find the area of the triangle/find the volume of the parallelepiped

How to find the find local max, min and inflection points from an integral?

Find condition that wedge may move and if it does, find acceleration?

Have dv/dx need to find dx/dt ? (have velocity w/ respect displace - find Accel?)

Search Tags