# pmf and support

• May 2nd 2009, 09:33 AM
logitech
pmf and support
In a smoking survey among boys between the ages of 12 and 17, 28% prefer to date nonsmokers, 1% prefer to date smokers and 21% don't care. Suppose 7 such boys are selected randomly and X equals the number who prefer to date nonsmokers and Y equals the number who prefers to date smokers.

A. Determine the joint p.m.f. of X and Y. Be sure to include the support of the p.m.f.
B. Find the marinal p.m.f. of X. Again include the support.

The support for A. I figured was \$\displaystyle O \le x \le 7, 0 \le y \le 7, 0 \le x+y \le 7.\$ The p.m.f. would be
combinations(X of 7)\$\displaystyle *\$combinations(Y of 7-X)\$\displaystyle *(0.78)^{x}*0.01^{y}*0.21^{(7-x-y)}\$

I can't figure out what values to use for x and y.

The support I put for B. is \$\displaystyle 0 \le x \le 7
\$ with p.m.f.=comb(X of 7)\$\displaystyle *(0.78)^{x}*(0.22)^{(7-x)}\$

I've been working on this problem, but I'm still really confused about how to perform the equations. Thank you for your help.
• May 3rd 2009, 03:50 AM
mr fantastic
Quote:

Originally Posted by logitech
In a smoking survey among boys between the ages of 12 and 17, 28% prefer to date nonsmokers, 1% prefer to date smokers and 21% don't care. [snip]

What about the other 50% ....?
• May 15th 2009, 04:35 PM
logitech
I'm sorry. The 28% was supposed to be 78% prefer to date nonsmokers. I'm not sure how the combination parts should be written to show the proper formula. Any help would be great!