Sattelhofsk
2022-06-26
Answered

Given that X and Y are RV supported on $[2,\text{}3]$ , If the correlation coefficient of ${X}^{t}$ and ${Y}^{s}$ is 0 for any $s,\text{}t\text{}\in \text{}[2,\text{}3]$ , then X and Y are independent.

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According to government data, the probability that an adull was never in a museum is 15%. In a random survey of 10 adults, what is the probability that at least eight were in a museum? Round to three decimal places

asked 2022-06-30

Consider a signal that is a sum of sinusoids, e.g.

$x(t)=Asin(at)+Bcos(bt)$

Is there an easy and general way to get an analytical solution for the autocorrelation of x(t)?

Is the best way to simply plug x(t) into the autocorrelation formula?

$x(t)=Asin(at)+Bcos(bt)$

Is there an easy and general way to get an analytical solution for the autocorrelation of x(t)?

Is the best way to simply plug x(t) into the autocorrelation formula?

asked 2022-09-23

Suppose we have a multivariate normal random variable $X=[{X}_{1},{X}_{2},{X}_{3},{X}_{4}{]}^{\top}$ . And here ${X}_{1}$ and ${X}_{4}$ are independent (not correlated). Also ${X}_{2}$ and ${X}_{4}$ are independent. But ${X}_{1}$ and ${X}_{2}$ are not independent. Assume that $Y=[{Y}_{1},{Y}_{2}{]}^{\top}$ is defined by

${Y}_{1}={X}_{1}+{X}_{4},\text{}\text{}{Y}_{2}={X}_{2}-{X}_{4}.$

If I know the covariance matrix of X, what would be the covariance matrix of Y?

${Y}_{1}={X}_{1}+{X}_{4},\text{}\text{}{Y}_{2}={X}_{2}-{X}_{4}.$

If I know the covariance matrix of X, what would be the covariance matrix of Y?

asked 2022-07-07

Now when we take ${Z}_{1}=X+{Y}_{1}$ and ${Z}_{2}=X+{Y}_{2}$ , what can we say about the correlation coefficient between ${Z}_{1}$ and ${Z}_{2}$?

For this case, is it possible to find the correlation coefficient as function of ${\sigma}_{x}$ and ${\sigma}_{y}$?

For this case, is it possible to find the correlation coefficient as function of ${\sigma}_{x}$ and ${\sigma}_{y}$?

asked 2022-07-19

Independent random variables $X,Y,X,U,V,W$ have variance equal to 1. Find $\rho (S,T)$ - the correlation coefficient of random variables $S=3X+3Y+2Z+U+V+W$ and $T=9X+3Y+2Z+2U+V+W$

asked 2022-08-18

Is there a good reason to use covariance and not correlation?

asked 2022-04-30

Two random variables, X and Y, have the joint density function:

$f(x,y)=\{\begin{array}{ll}2& 0<x\le y<1\\ 0& ioc\end{array}$

Calculate the correlation coefficient between X and Y.

$f(x,y)=\{\begin{array}{ll}2& 0<x\le y<1\\ 0& ioc\end{array}$

Calculate the correlation coefficient between X and Y.