# proof

1. ### How to derive multivariate normal pdf from matrix normal pdf?

I am working on the proof part in Definition section of https://en.wikipedia.org/wiki/Matrix_normal_distribution. I can understand what s going on, except for the last part how inv(V(kron)U) becomes inv(U) for multivariate distribution. is there any source you can help me with how to get...
2. ### Proof of Kalman filter related lema

Hi... Can you please provide a proof of the formula given on the attached image?
3. ### Prove: Birth-death chain has stationary distribution -> satisfy detail bal. equations

I'm working my way through a course in stochastic processes but came across this Lemma in my coursebook where they didn't show the working (Lemma 8.5). I'm not familiar with doing proofs and it isn't taught in any of my courses but I can read/understand them, how did they reach the conclusion of...
4. ### Bayesian statistics proof question

I know that if the prior distribution is chosen to be a continuous uniform distribution, then the exact posterior distribution will simply the normalized version of the likelihood function. I was wondering how i would write this out as a proof?
5. ### How to show that b1 and SSE are independent?

under normal sampling zero covariance implies independence. So I tried to solve COV(b1,SSE). COV(b1,SSE) = E[(b1-beta1)(SSE-sigma^2*(n-2))] =... =E(b1*SSE)-beta1*sigma^2*(n-2) But I don't know how to solve E(b1*SSE). Do you know how to solve this? Or did I do something wrong?:confused::(
6. ### proving regression with dummy variables gives same estimates as separate models

See attachment for problem description: To prove this I started by using: vector of Beta estimates for category k = [Bk], matrix of estimates for category k = [Xk], Y estimates for category = [Yk]. 1. Find betas for single category: Calculating [Ba] = (Xa' * Xa)inv * (Xa' *Ya) for the 2. Find...
7. ### Sum of squares model proof

Hello everyone :-) I'm trying my best to prove the formula for the sum of squares model (please excuse how badly i'm going to write this) Betahat'X'Y-n(ybar)squared so far i have that it is equal to (yhat-ybar)'(yhat-ybar) so i just need to show that they equal eachother. I know...
8. ### Proof of asymptotic normality of MLE

If someone has seen these theorems I would appreciate some help in understanding a part of a certain proof. The usual way to show that \sqrt{n} \left( \hat{\theta}-\theta_0 \right) \xrightarrow{D} N \left( 0, \frac{1}{I \left( \theta_0 \right)} \right) is to expand l \prime \left( \theta...
9. ### Proof of constistency of Maximum Likelihood Estimators (MLE)

Hi all, I would appreciate some help comprehending a logical step in the proof below about the consistency of MLE. It comes directly from Introduction to Mathematical Statistics by Hogg and Craig and it is slightly different than the standard intuitive one that makes use of the Weak Law of...
10. ### Proof the sum of two CDF's is a CDF.

This is a question my instructor asked in the last midterm exam but nobody was able to solve and he's suggesting it may come out again in the finals: If F(x) and G(X) are two CDF's, prove that H(X) is also a CDF if H(X) = F(X)+G(X)-F(x)G(X) He said something about right...
11. ### Multiple Linear Regression Proof

Hi everyone, I am enrolled in a regression analysis course at university and the prof really loves to ask for proofs on his assignments. Unfortunately, he never does any in class, and no one at the help centres on campus can ever figure out his problems either. Here is the one I am...
12. ### Sst= ssw+ssb

Hi everyone, I have this problem to solve. It's been a while since I tried to figured out how to do, but I am totally lost. Here it is. Prove SST= SSW+SST in one-way Anova (one factor). Σ ( xi - x̄ )² = Σ (xi - x̄ + x̄ k - x̄ k ) ² Hint: Σ [ ( xi - x̄ k ) + ( x̄ k - x̄ )]² Where...
13. ### cumulative distribution function problem

I have this question I am trying to get through but i keep coming into trouble. The question is: Show that the cumulative distribution function from a uniform distribution of the random variable is Fx(y) = (y-a) / (b-a) for some a < y < b I've started the question but have become stuck...
14. ### How to prove that the expectation and variance of a Poisson random variable = lambda?

This probably has an easy solution, but I was wondering if anybody could help me solve and explain these two questions: (a) Show that the expectation of the random variable is E(X) = lambda (b) Show that the variance of the random variable is Var(X) = lambda Any help would be very...
15. ### Arithmetic proof of predicted values

Maybe the title of this thread should be: Arithmetic proof of predicted values or Why you shouldn't let stats lie dormant in your life for 7 years! :D I'm boning up on stats and reviewing some introductory text that looked interesting. One that I'm working through is Doing Bayesian...