1. ## Discrete Random Variable

The median annual income for the heads of households in a certain city is $44,000. Four such heads of households are randomly selected for inclusion in an opinion poll. Let X be the number (out of four) who have annual incomes below$44,000.

Find the probability distribution.

$\displaystyle \displaystyle\frac{\binom{4}{x}\binom{4}{4-x}}{\binom{y}{4}}, \ \ \ x=0, \ 1, \ 2, \ 3, \ 4$

I don't know what y is.

2. Notice that they said "median" and not "mean." So it's binomial with p = 0.5 and n = 4.

3. Originally Posted by dwsmith
The median annual income for the heads of households in a certain city is $44,000. Four such heads of households are randomly selected for inclusion in an opinion poll. Let X be the number (out of four) who have annual incomes below$44,000.
As Random_Variable points out this is a binomial RV with p=0.5 and n=4 (because $44,000 is the median) Find the probability distribution.$\displaystyle \displaystyle\frac{\binom{4}{x}\binom{4}{4-x}}{\binom{y}{4}}, \ \ \ x=0, \ 1, \ 2, \ 3, \ 4$I don't know what y is. This last part makes no sense is it supposed to be related to the first part? How? CB 4. Originally Posted by CaptainBlack As Random_Variable points out this is a binomial RV with p=0.5 and n=4 (because$44,000 is the median)

This last part makes no sense is it supposed to be related to the first part? How?

CB
The probability distribution p(x) is for x = 0, 1, 2, 3, 4.

So my numerator would be 4 choose x times the 4 choose 4-x divided by the sample population which would be population choose 4 but I don't know the population.

5. Originally Posted by dwsmith
The probability distribution p(x) is for x = 0, 1, 2, 3, 4.

So my numerator would be 4 choose x times the 4 choose 4-x divided by the sample population which would be population choose 4 but I don't know the population.
That is not the mass function for the binomial distribution.

CB

6. Originally Posted by CaptainBlack
That is not the mass function for the binomial distribution.

CB
Then I don't know what I am supposed to do.

7. Originally Posted by dwsmith
Then I don't know what I am supposed to do.
As we have said $\displaystyle$$X$ is a RV with a binomial distribution $\displaystyle B(p=0.5, n=4)$

$\displaystyle pr(X=x)=b(x;p,n)=\dfrac{n!}{x!(n-x)!}p^x(1-p)^{n-x};\ \ \ \ n=4, p=0.5; x=0,1,..4$

CB