 745
 31
 Problem Statement
 "Let ##Y_i## be independent Bernoulli r.v.'s. Let ##T=1## if ##Y_1=1## and ##Y_2=0## and ##T=0## otherwise. Let ##W=\sum Y_i##. Prove that ##P(T=1W=w)=\frac{w(nw)}{n(n1)}##.
 Relevant Equations

##P(AB)=\frac{P(A\cap B)}{P(B)}##
An answer from another part in the problem: ##E(T)=p(1p)##
##P(T=1W=w)=\frac{P(\{T=1\}\cap\{W=w\})}{P(W=w)}=\frac{\binom {n2} {w1} p^{w1}(1p)^{(n2)(w1)}}{\binom n w p^w (1p)^{nw}}=\frac{(n2)!}{(w1)!(nw1)!}\frac{w!(nw)!}{n!}\frac{1}{p(1p)}=\frac{w(nw)}{n(n1)}(p(1p))^{1}##.
I cannot seem to get the terms with ##p## out of my expression.
I cannot seem to get the terms with ##p## out of my expression.