each element of a sequence of binary data is either 1 with probability p or 0 with probability 1-p. a maximal sub sequence of consecutive value having identical values is called a run. Ex. in 1,1,0,1,1,1,0 first run=2 second run= 0
find expected length of the first run
conditioning on the first run
E[x]=E[x]Y=y]
when y=1 i saw this as gemotric distribution with probability of success= p and its mean 1/(p)
and when y=0, same thing but with probability of success= 1-p and mean 1/(1-p)
And E(x)= Ex]y=0 * P(y=0) + Ex]y=1 * p(y=1)
= p* (1/p) + (1-p)*(1/(1-P))=
1+1=2
but i have a bad feeling!