Hello everybody,
I have two questions on conditional expectation w.r.t (Polynomial) OLS:
Let X_t be a random variable and F_t the associated filtration, Vect_n{X_t} the vector space spanned by the polynomials of order {i, i<=n }, f(.) one function with enough regularity. I am wondering how...
This result isn't in our book, but it is in my notes and I want to make sure it's correct. Please verify if you can.
Homework Statement
I have two I.I.D random variables. I want the conditional expectation of Y given Y is less than some other independent random variable Z.
E(Y \...
I need help about conditional expectation for my research. I get stucked on this point. Could anyone show me how to prove that:
"Let E[|Y|]<∞. By checking that Definition is satisfied, show that if Y is measurable F0, then E[Y|F0]=Y."
Def: Let Y be a random variable defined on an underlying...
Let X, Y be independent exponential random variables with means 1 and 2 respectively.
Let
Z = 1, if X < Y
Z = 0, otherwise
Find E(X|Z) and V(X|Z).
We should first find E(X|Z=z)
E(X|Z=z) = integral (from 0 to inf) of xf(x|z).
However, how do we find f(x|z) ?
[SOLVED] Conditional Expectation
I'm trying to understand the following proof I saw in a book. It says that:
E[Xg(Y)|Y] = g(Y)E[X|Y] where X and Y are discrete random variables and g(Y) is a function of the random variable Y.
Now they give the following proof:
E[Xg(Y)|Y] = \sum_{x}x g(Y)...
I need help in solving the following problem:
Let X be uniformly distributed over [0,1]. And for some c in (0,1), define Y = 1 if X>= c and Y = 0 if X < c. Find E[X|Y].
My main problem is that I am having difficulty solving for f(X|Y) since X is continuous (uniform continuous over [0,1])...
Any hints on how to solve for E(Y|X) given the ff:
Suppose U and V are independent with exponential distributions
f(t) = \lambda \exp^{-\lambda t}, \mbox{ for } t\geq 0
Where X = U + V and Y = UV.
I am having difficulty finding f(Y|X)...
Also, solving for f(X,Y), I am also having difficulty...
Is it possible to solve for E(Y) and var (Y) when I am only given the distribution f(Y|X)?
I can solve for E(Y|X). But is it possible to find E(Y) and var(Y) given only this info?
I found this question in a book:
Two palyers A and B alternatively roll a pair of unbiased die. A wins if on a throw he obtain exactly 6 points, before B gets 7 points, B wining in the opposing event. If A begins the game prove that the probability of A winning is 30/61 and that the expected...