I've got a tricky computational statistics problem and I was wondering if anyone could help me solve it.
Okay, so in your left pocket is a penny and in your right pocket is a dime. On a fair toss, the probability of showing a head is p for the penny and d for the dime. You randomly chooses a...
Hey guys, I'm trying to find a conditional distribution based on the following information:
##Y|u Poisson(u \lambda)##, where ##u~Gamma( \phi)## and ##Y~NegBinomial(\frac{\lambda \phi}{1+ \lambda \phi}, \phi^{-1})##
I want to find the conditional distribution ##u|Y##
Here's what I've got so...
Hey guys, I was wondering if you could help me out with a question I've got, I really don't know where to go or really where to start! Here's the question:
Let S be a subspace of a finite dimensional vector space V. Show that there exists a Linear Mapping L: V → V such that the kernel of L is...
Ok, but there's this example in my textbook:
\sum^{n=1}_{infinity}(1/2)^{n}=\frac{1/2}{1-(1/2)}=1
"The series is a geometric series with a=1/2 and r=1/2"
I'm confused as to how a=1/2
Oh! Everything would cancel out except a - ar^n
S - r*S = a - ar^n
...
S = a(1 - r^n)/(1-r)
which explains why -1<r<1 since the limit n->inf r^n would diverge above 1
But judging by what everyones been saying, I'm assuming if n=1, then the sum is a/(1-r) and if it starts at 0 you have to multiply everything by r, making the actual sum ar/(1-r)
EDIT: n=1 to infinity of course