Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [variance]

For questions regarding the variance of a random variable in probability, as well as the variance of a list or data in statistics.

In probability and statistics, variance is a measure of spread among the possible values of a random variable or a list of values.

More information can be found here.

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variance of standard sample deviation in a normal distribution

I need help. I Know that using Fisher Lemma, we know that in a normal distribution $ Var(\hat{\sigma^2})= \frac{2\sigma^4(n-1)}{n^2}$, since $\frac{n\hat{\sigma^2}}{\sigma^2}\approx \chi^2_{n-1}$. I need now to calculate $Var(\hat{\sigma})$, but i…
Javi Gomez
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When calculating probability in Roulette why don't we add the probabilities of win and loss?

In a game of roulette if you bet \$1 you either win \$35 with a probability of 1/38 or loose \$1 with a probability of 37/38. Thus I calculate the chance of winning on a single play as $E(W)=35/38 -37/38 = -1/19$ It has been explained to me that we…
Kirsten
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Analogous version of $\operatorname{var(X+cY)} = \operatorname{var}(X) + c^2\operatorname{Var}(Y)$ for vectors of uncorrelated random variables?

Is there an analogous version of $\operatorname{var(X+cY)} = \operatorname{var}(X) + c^2\operatorname{var}(Y)$ for vectors of uncorrelated random variables ($X$ and $Y$ are random variables here)? For example, consider…
user5965026
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Calculation of variance

Suppose E(X|Y) and that a figure illustrates expected salary as a function of gender and that it shows that the mean for women is $2500 \$$ and for men is $3500\$$. If $50\%$ are women and $50\%$ men, the variance is 250 000. How to get there, how…
ASKING
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Find variance of $-3X+5$ given $E(X)$ and $E(X(X-2))$

Suppose that $X$ is a discrete random variable with $E(X) = 1$ and $E[X(X −2)]= 3$. Find $Var(−3X + 5)$. $$E[X(X-2)]=E(X^2-2X)=3$$ $$Var(-3X+5)=E[(-3X+5-1)^2 ]=E(9X^2-24X+16)$$ $$E(9X^2-24X+16)=9E(X^2-2X)-6E(X)+16=37$$ I found the answer to be…
LadymadeStar
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Variance of values of a function over an interval

I want to find out the spread of values that a particular function can take over an interval. How do I calculate the variance of the values of the function over that interval? For example, if I want to calculate the mean value of the function over…
Mouli Modak
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How to calculate Var(x)?

How do I calculate Var(x) if I know that $X | Y = y \sim N(y,1)$ and the PDF of Y is given by $$ f_Y(y) = \begin{cases} 3y^2 \ \ \ \text{for} \ 0 < y < 1 \\ 0 \ \ \ \ \ \ \ \text{othwerwise} \end{cases} $$ I thought about using the law of total…
Mathias
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Variance of 3 point shots

Suppose that each time Michael Jordan takes a 3-point shot, he has a 37% probability of success, independent of all other attempts. If Jordan takes seven 3-point shots in a game, what is the variance of the total number of points he scores from…
Wayne L
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(Why) Do N trials of a B.P. reduce variance by a factor of N?

This question arrises from the lecture of a book called "Data mining" by Witten and Frank. I try to understand a statement and there is one point I just do not understand nor do I find any explanation: We are considering a Bernoulli process which…
croessler
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How to use the Weak Law of Large Numbers to show this?

Let $X_1,...,X_n$ be an iid (independent and identically distributed) sample with mean $ \mu $ and variance $\sigma^2$. We can use this conclusion ：$ (n-1)S^2 = \sum_{i=1}^n (Xi-\overline X)^2 = \sum_{i=1}^n (Xi-\mu ) ^2 - n(\mu-\overline X) ^2 …
gong.y
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Understanding the formula of sample variance

So i know that the sample variance generic formula is : $$ S_n^2=\frac{1}{n-1}\sum_{i=1}^n(X_i-\overline{X}_n)^2. $$ And i have this question : $Y$ takes values of $0$ and $1$. $\operatorname{Pr}(Y=1)=p=0.78$ $\operatorname{Pr}(Y=0)=1-p=0.22$ I do…
GGGG
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Variance random variables

someone can explain me why the difference of 2 random variables indipendent is the sum of 2 random variables and not the difference? So, why Var(X-Y) = Var(x) + Var(y) ?
Andrea Boom
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Variance in different measurements

What is the best way to convert variance in one measurement unit to variance in another measurement unit? For example: The variance of the heights of the mango trees in your garden is 13 square feet. What will be the variance in yards?
cyclops
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How to calculate the variance of a continuous distribution function but with a mass point?

I have a continuous distribution function, but it has a mass point at the upper bound, say with a probability of p>0. How to calculate its variance?
Adam
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Finding Variance of joint probability function

I need help in finding the variance of a joint probability function. The probability density function in this case is $f(x)$ which is created by $$\frac{125x^2}{18},\; 0\le x\le 0.6,\;\frac{9}{10x^2},\; (0.6\le x\le 0.9), \text{ and } 0 \text{…
Deep Patel
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