How do I approach the following problem while only knowing the PSD of a Gaussian random sequence (i.e. I don't know the exact distribution of $V_k$)? Or am I missing something obvious?
Problem statement:
Thoughts:
I know with the PSD given, the autocorrelation function are delta functions due...
For part (c) I think you are right, I think I mixed it up with the one output per second output from the rain gauge. So, I believe the final answer should be ##Bernoulli(e^{-3})##.
So, for part (d), you think it is NegBin, but I'm not not sure what the p and k parameters should be (see notes...
Sorry, I meant parameters (i.e. the lambda in Poisson(3) ). I'm quite sure of my answers for parts a and b but the rest is making me confused. Would you be willing to check and guide through mistakes?
I’m quite thrown off with how the rain gauge outputting a random sequence at a rate of one every second comes into play in this problem, especially when specifying the partners for the RVs.
Hello. I would like to kindly request some help with a multi-part problem on identifying random processes as an intro topic from my stats course. I’m fairly uncertain with this topic so I suspect my attempt is mostly incorrect, especially when specifying the parameters, and I would be grateful...
Hi all, I have a problem on linear estimation that I would like help on. This is related to Wiener filtering.
Problem:
I attempted part (a), but not too sure on the answer. As for unconstrained case in part (b), I don't know how to find the autocorrelation function, I applied the definition...
Hello all, I would appreciate any guidance to the following problem. I have started on parts (a) and (b), but need some help solving for the coefficients. Would I simply take the expressions involving the coefficients, take the derivative and set it equal to 0 and solve? I believe I also need...
Hello all, I am wondering if my approach is correct for the following problem on MSE estimation/linear prediction on a zero-mean random variable. My final answer would be c1 = 1, c2 = 0, and c3 = 1. If my approach is incorrect, I certainly appreciate some guidance on the problem. Thank you...
I am having difficulties setting up and characterizing stationary and ergodicity for a few random processes below. I need to determine whether the random process below is strict-sense stationary (SSS), whether it is wide-sense stationary (WSS), and whether it is ergodic in the mean. All help is...
Thank you for your help. I realize the mistakes now. I had the formula wrong originally by using the mean of y in stead of mean of x hence had the extra factor of +2. So yes the answer now makes sense: when y=7, then x=5 which is expected.
The parameters I used were ##µ_X = 5, µ_Y = 7, σ_X = √5, σ_Y = √7, and ρ = √(5/7) ##
Using the formula above, I get
##E(X | Y = y) =µ_X +ρσ_X( (Y-µ_Y ) / √7) = 5 + √(5/7)√5 ( (y-7 ) /√7) ##
and then ## E(X | Y = y) = y - 2 ## but that turns out to be incorrect.
Good point on part (iii) with the units. Hmm I would note down both for my studies
Part (c) is an error on my part due to copy/pasting. You are correct in that formula could contain a ##y##
I believe the formula should also say ##u_x## so if I make those corrections, I get a final answer of...
My mistake on (i)
X is either non-zero or it isn't. It's non-zero with probability p=1-e^(-5)
Thus it's Bernoulli with parameter p -> X is Bern( 1-e^(-5) ) should be the correct answer I hope
(ii) Z is the number of events in [5,7], since X and Y overlap by 5 us, so Z is Poisson(2)