# Homework Help: Statistics pmf

1. Feb 27, 2006

### happyg1

Hi,
I know this isn't hard, but I have a block on it.
Here's the question:
Let $$f(x)=1/6, x=1,2,3,4,5,6$$ zero elsewhere be the pmf of a distribution of the discrete type. Show that the pmf of the smallest observation of a random sample of size 5 from this distribution is:
$$g_1(y_1)=\left(\frac{7-y_1}{6}\right)^5-\left(\frac{6-y_1}{6}\right)^5,y_1=1,2,3,4,5,6$$

I know I'm looking for the pmf of the minimum, which is the y_1, and I did this:
$$P(Y_1=y_1)=P(Y_1\leq y_1)-P(Y_1<y_1)$$
I'm having trouble seeing why there's a 7 in the solution. I'm missing something.
I know that wheneve I get the probabilities of each piece, they will be to the 5th power because there's 5 observations in the sample and we multiply the probabilities together. What the probabilities are is the part that has me confused.
We've been focusing on continuous problems for so long I can't wrap my mind around this.
Any hints or pointers will be appreciated.