# 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.

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### Find the mean and the variance of $X(1)$ for stochastic differential equation: $dX(t)=-1.5X(t)dt+0.85dW(t)$ with $X(0)=0.7$

Suppose that $X(t)$ satisfies $\hspace{5cm}$ $dX(t)=-1.5X(t)dt+0.85dW(t)$ with $X(0)=0.7.$ Find the mean and the variance of $X(1).$ I know that $E[X(1)]$ will result in mean and $E[(X(1))^{2}]$ in ...
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### Bernoulli Model: Help calculating variance of asset price?

I'm currently looking at the Bernoulli Model for an asset, with spot price $S_{0}$, which can rise to $uS_0$ with probability $p$ or drop to $dS_0$ with probability $q = 1-p$, over a time of $\delta t$...
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### Calculate the expectation and variance for normal distribution [closed]

I am solving a question which is about distribution but it is confusing as I am new in the course of applied data analysis. how we calculate the expectation and variance when we have this given ...
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### Do the sample coefficients of variation follow a specific distribution when a lot of samples are taken?

I am measuring the coefficient of variation after a process takes place, and I do not know the population distribution. I would like to find the probability the coefficient of variation is smaller ...
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### When do we add variance and when do we use $Var(cx) = c^2Var(x)$?

This is a problem that I'm working on: A yoga studio is trying to estimate total class sales for next year. They assume that: Between 10 and 14 people attend each class (uniformly distributed) Each ...
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### Variance of nested random variables (e.g. dices)

I have a set of independent but not identically distributed dice $D_0, \dots, D_n$, with mean values $\mu_i$ and variances $\sigma_i$. Now i decide to roll one dice at random with probability $p(D_i)$,...
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### Flajolet & Sedgewick: How to compute the variance of the number of cycles in a random permutation?

I am reading the book Analytic Combinatorics 4ed by Sedgewick and Flajolet. On page 160 at Example III.4 the authors derive the variance of the number of cycles in a random permutation. I can follow ...
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### Does the population variance equal the variance of a single observation?

According to Wikipedia, the standard error $\sigma^-_x$ of a sample mean can be computed by $\frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the standard deviation of a statistical population and $n$ is ...
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### Calculate $E(X^4 )$ and let $s ∈ R$ be a constant. Calculate $E(e^{sX}).$

X is a normal random variable such that X~N{µ, σ$^2$}. To find $E(X^4 )$ I took $Y=X^2$ hence $E(X^4)=E(Y^2)=Var(Y)+E[Y]^2=Var(Y)+ (σ^2+µ^2)^2$ however I'm unable to find an adequate substitution for ...
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### Conditional variance of Y given X when y is a continuous function of x

Technically the problem term would be $E[Y^2|X]$ For simplicity, let us for a minute assume that $y = a + bx$ Is it mathematically correct to write: $E[Y^2|X] = E[(a+bx)^2]$, and if so why? And how ...
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I have a random variable $X=a_1X_1+a_2X_2 + \ldots a_kX_k$ where $X_i \sim Bern(q)$, $X_i \perp X_j, \forall i,j\in \{1,2\ldots,k\}$. Also $\sum_{i=1}^{k} a_i=k$ and \$a_i \in \mathbb{N} \bigcup \{0\...