Strong Correlation Examples You Can Find Here!

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 $σ_{x}$ and $σ_{y}$ ?

Gretchen Schwartz 2022-07-07

Show that the correlation coeffcient of $x_{i} - \bar{x}$ and $x_{j} - \bar{x}$ is $- (n - 1)^{- 1}$

orlovskihmw 2022-07-03

Let the joint distribution of (X, Y) be bivariate normal with mean vector $(\begin{matrix} 0 \\ 0 \end{matrix})$ and variance-covariance matrix
$(\begin{matrix} 1 & 𝝆 \\ 𝝆 & 1 \end{matrix})$ , where $- 𝟏 < 𝝆 < 𝟏$ . Let $𝚽_{𝝆} (𝟎, 𝟎) = 𝑷 (𝑿 \leq 𝟎, 𝒀 \leq 𝟎)$ . Then what will be Kendall’s $τ$ coefficient between X and Y equal to?

Reed Eaton 2022-06-30

Consider a signal that is a sum of sinusoids, e.g.
$x (t) = A s i n (a t) + B c o s (b t)$
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?

Sattelhofsk 2022-06-26

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

Averi Mitchell 2022-06-16

Can I maximize the correlation between a linear combination of variables and some other variable?

Amber Quinn 2022-06-15

Why is the following true for the covariance $c o v (X, Y)$ and variances $V a r (X)$ , $V a r (Y)$ of two rvs X and Y:
$\frac{C o v (c X, Y)}{\sqrt{V a r (c X) V a r (Y)}} = \frac{c C o v (X, Y)}{\sqrt{c^{2} V a r (X) V a r (Y)}} = \frac{C o v (X, Y)}{\sqrt{V a r (X) V a r (Y)}}$

Cody Lowe2022-05-11

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

Merati4tmjn 2022-05-09

It is known that $ρ$ , the pearson correlation, is a measure for the linear dependence of two random variables say X, Y. But can't you say just transform X and Y such that we have,
$ρ_{X, Y} (f (X), g (Y))$
where f, g are non-linear functions such that it measures other kinds of dependce (take for example $f (s) = g (s) = s^{2}$ for quadratic dependence).

juniorychichoa70 2022-05-02

I am getting $f_{X, Y} (x, y) = f_{X} (x) f_{Y} (y)$ even if the correlation coefficient $ρ \neq 0$

znacimavjo 2022-05-01

Suppose you have two sequences of complex numbers $a_{i}$ and $b_{i}$ indexed over the integer numbers such that they are convergent in $l^{2}$ norm and a has norm greater than b in the sense
$\infty > \sum_{i} | a_{i} |^{2} \geq \sum_{i} | b_{i} |^{2} .$
Suppose moreover they are uncorrelated over any time delay, meaning
$\sum_{i} a_{i} \bar{b_{i - n}} = 0 \forall n \in Z .$
Is it true that the polinomial $a (z) = \sum_{i} a_{i} z^{- i}$ is greater in absolute value than $b (z) = \sum_{i} b_{i} z^{- i}$ for any unit norm complex number z?

gaitaprepeted05u 2022-04-30

Two random variables, X and Y, have the joint density function:
$f (x, y) = {\begin{cases} 2 & 0 < x \leq y < 1 \\ 0 & i o c \end{cases}$
Calculate the correlation coefficient between X and Y.

When you are dealing with statistics and probability, inferential statistical data will be one of those complex tasks where you will use the correlation coefficient calculator for your management data or the lab experiments. As you can learn from the questions that are being asked when working on correlation tasks, the range of practical applications is almost endless. See various correlation problems examples below and take a step-by-step approach as it will help you to understand the probability aspect and adjust the variables accordingly. The most important is to provide verbal explanations for your sample groups and explain your methods.

Inferential Statistics

Correlation: Practical Examples & Insights