All Questions
10
questions
2
votes
1
answer
97
views
Variance recursion formula in Galton-Watson process
Consider a Galton-Watson process with expected offspring $\mathbb{E}[\xi]=\mu<\infty$ and variance $\text{Var}(\xi)=\sigma^2<\infty$ where the offspring in generation $t\in\mathbb{N}$ is given ...
0
votes
2
answers
68
views
How to take the variance of a second order expansion? $\text{Var}\left[aX+bY+cXY+mX^2+nY^2\right]$
How to take the variance of a second order expansion? $\text{Var}\left[aX+bY+cXY+mX^2+nY^2\right]$
Let say we have 5 real-valued constant parameters $\{a,\ b,\ c,\ m,\ n\}$, and two random variables $...
- 1,356
0
votes
1
answer
236
views
Calculate variance of period-to-period change of Markov chain given transition matrix.
In the process of working on a project, I am faced with the following question:
let us say our transition matrix $P$ is given by:
\begin{bmatrix}
P_{1,1} & P_{1,2} & P_{1,3} & P_{1,4} \...
user888043
0
votes
1
answer
745
views
Third Moment of Expectation?
I'm trying to find the $E[X^3]$ in terms of $\mu$ and $\sigma^2$.
I found online somewhere that it's
$\mu^3 + 3\mu\sigma^2$.
But there's no proof or explanation anywhere for it. Could someone ...
- 1
0
votes
1
answer
121
views
Finding variance of a random variable given by two uncorrelated random variables
a) Let $X$ and $Y$ be two uncorrelated random variables. Assume $Var(X) = 1.55$ and $Var(Y) = 0.8$. What is the variance of the random variable $Z = -4X + 5Y - 6$?
b) What if $X$ and $Y$ are ...
- 1,033
2
votes
2
answers
124
views
Variance of $\int_0^1X(t)dt$
Let $X(t)$ be a stationary random variable with expected value $E[X(t)] = m$ and covariance function $r_X(\tau) = 2e^{-|\tau|}$.
I'm asked to calculate the variance of $\int_0^1X(t)dt$,
$$V[\int_0^...
- 1,059
2
votes
3
answers
135
views
Covariance for stochastic variables
if $X$ and $Y$ are stochastic variables with $\operatorname{Var}(X)=1.34$ and $\operatorname{Cov}(X,Y) = 0.64$, find $\operatorname{Cov}(2X, 3X+2Y)$. No ideas on this one, as I don't see any way of ...
- 917
1
vote
0
answers
56
views
Variance of following process
I got stuck to find the variance of the following AR(1) process. It looks really simple but I just can't solve it.
The process is
$x_{t+1}$ = a + b$x_{t}$ + c$\sqrt{x_{t}}$$\epsilon_{t+1}$
where $...
- 31
0
votes
1
answer
56
views
How to compute basic statistics of the time series $Y_j = A \sin(\theta \times j) + Z_j$
Given the time series:
$$Y_j = A \sin(\theta \times j) + Z_j$$
where
A random variable with mean $0$ and variance $1.$
Z white noise with mean $0$ and variance $\sigma^2$.
$\theta \in \left\{0, \...
- 225
1
vote
1
answer
720
views
Conditional variance of simple random walk
Let $\{X_i \mid i \in \mathbb{N} \}$ be a sequence of independent and identically distributed random variables with probability mass function given by:
$$
P(X_i = x)=
\begin{cases}
p, & \text{if }...
- 1,049