Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Homework Help
Precalculus Mathematics Homework Help
Geometric distribution Problem
Reply to thread
Message
[QUOTE="throneoo, post: 4902808, member: 384822"] [h2]Homework Statement [/h2] a man draws balls from an infinitely large box containing either white and black balls , assume statistical independence. the man draws 1 ball each time and stops once he has at least 1 ball of each color . if the probability of drawing a white ball is p , and and q=1-p is that of drawing a black ball , what is the: a) average no. of balls drawn b)average no. of white/black balls drawn c)variance of no. of white/black balls drawn[h2]Homework Equations[/h2] Defining N,W,B as the total no. of balls , no. of white/black balls respectively , the probability generating functions (pgf) for N,W,B are respectively θ(x)=Σpx(qx)^B from B=1 to infinity + Σqx(px)^W from W=1 to infinity =Σ(p(qx)^B+q(px)^B)x from B=1 to infinity =pqx^2((1-qx)^-1+(1-px)^-1) α(x)=Σq(px)^W from W=1 to infinity =pqx/(1-px) β(x)=Σp(qx)^B from B=1 to infinity =pqx/(1-qx) [h2]The Attempt at a Solution[/h2] Thus , <N>=dθ/dx at x=1 =p/q + q/p +1 <W>=dα/dx at x=1 =p/q <B>=dβ/dx at x=1 = q/p <W^2>=d[x*dα/dx]/dx at x=1 =p(p+1)/q^2 <B^2>=d[x*dβ/dx]/dx at x=1 =q(q+1)/p^2 Var(W)=<W^2>-<W>^2=p/q^2 Var(B)=<B^2>-<B>^2=q/p^2 [B]4. Question[/B] my concern is , why doesn't <N>=<W>+<B> ? It seems to contradict N=W+B . Also , the expression I've got for <N> has a local minimum at (p,<N>)=(0.5,3) which is also a bit weird [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Precalculus Mathematics Homework Help
Geometric distribution Problem
Back
Top