# 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.

1,172 questions
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### We flip a coin until a tail or five heads in a row occur. What is the number of expected flips?

We flip a coin until a taild or five heads in a row occur. What is the number of expected flips? I have tried to solve this by first defining 2 random variables: X ...
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### Proof of Variance of the Irreducible Error

In Introduction to Statistical Learning, given the general form of a quantitative response between a set of predictor variables and a target variable $$Y=f(X)+\epsilon$$ and the general form for a ...
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### Calculating Expectation and Variance

I think I have an idea of how to solve these problems, but I keep getting stuck. Any help would be greatly appreciated! Also, sorry I know I messed up the formatting with the exponents in the problems....
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### Delta Method: Estimate the Variance of $T$

Let $X = (X_1,\ldots,X_n)$ be a random sample, where $X_1 \sim \mathrm{Bern}(p)$. Let $\lambda = e^p$. Question: By law of large numbers, $T=e^{(\bar{X})}$ is a consistent estimator for $\lambda$, ...
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### Minimum variance portfolio problem

So the question asks: There are N (N > 1) stocks with the same variance $σ^2$ and the same pairwise correlation coeﬃcient γ (i.e. $c_ij$ = γ for all i = j. γ is a given constant such that 0 ≤ γ < ...
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### confused about meaning of a expectation of a function

https://en.wikipedia.org/wiki/Bias%E2%80%93variance_tradeoff#Derivation well,in the "Derivation" part of the wiki link. i don't figure out why $E(f)=f$, does it imply that the function $f$ is ...
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### Is this a special probability distribution?

Does the distribution function: $\frac{1}{\theta}e^\frac{-y}{\theta}$ Have a special name? If not, how can I find the variance? I keep running into a dead end when I try.
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### Recalculate Standard Deviation

I know how to calculate a standard deviation when given a set of values. You must calculate the mean, then square the difference of each value between the mean to get the variance. Lastly, the ...
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I feel like this might be really hard but I'm not sure. If you get this, you just might be a genius.. $X \sim \mathcal N(\mu_1,\sigma_1)$, $Y \sim \mathcal N(\mu_2,\sigma_2)$, $Z \sim \mathcal N(\... 1answer 29 views ### Difficulty in finding marginal distribution Let$X=(X_{1},X_{2})$have joint pdf.$$f(x_{1},x_{2})=\begin{cases}\frac{e^{-\frac{x_{2}^2}{2}}}{x_{2}\sqrt{2\pi}},\ &\text{if}\ 0<|x_{1}|\le x_{2}<\infty.\\0,\ &\text{otherwise} \end{... 1answer 499 views ### Sample variance: degree of freedom argument In sample variance we divide by n-1 and not n. I know a couple of arguments for this - one is that this is sort of a normalization to ensure that the expected value of sample variance is equal to ... 2answers 242 views ### Find \text{Var}(N) where P(N = n|Y = y) is \text{Possion}(y); Y is a gamma with parameters (r,\lambda) The question is as follows: Suppose that the conditional distribution of N, given that Y = y, is Poisson with mean y. Further suppose that Y is a gamma random variable with parameters (... 1answer 713 views ### The symbols for variance and covariance I learned to denote the variance of x as \sigma_x^2, and the covariance of x and y as \sigma_{x, y}. The covariance of x and x is then \sigma_{x, x}, but because that it just the ... 1answer 2k views ### What does “variance unity” mean?: “A normal distribution with mean \mu and variance unity”. I've just come across the sentence: "Suppose you have the sample \ldots from a normal distribution with mean \mu and variance unity." What does variance unity mean? Variance equals 1? I can't ... 0answers 289 views ### Calculating the variance of an average of N iid random variables I'm having some problems proving that the variance of an average of N iid random variables is equal to \frac{1}{N}\text{Var}[X_1], where X_1 is one of the considered random variables. Formally, ... 0answers 25 views ### Deriving variance In kinetic methods of analysis, the rate of appearance of products is often used to infer the initial concentration of a reactant or substrate. The problem with this method is that often the rate ... 0answers 92 views ### Variance of the sum of a random subset [closed] Let A be the group of whole numbers in the range [0, n). We choose uniformly at random from all subsets of size k (0 < k < n). The mean of the sum of the subset is \frac{n-1}{2} k. ... 2answers 6k views ### Variance of Negative Binomial Distribution (without Moment Generating Series) Given the discrete probability distribution for the negative binomial distribution in the form$$P(X = r) = \sum_{n\geq r} {n-1\choose r-1} (1-p)^{n-r}p^r$$It appears there are no derivations on ... 1answer 1k views ### Random Variables, Minimize Variance The variance of X_1, X_2 are 1 and 4, and the correlation coefficient p=-0.3 1)Calculate the variance of Z_1 = 2X_1+X_2 2)Calculate the value of a that minimizes the variance of Z_2 = aX_1+(1-... 0answers 425 views ### Expected value of mean squares. ANOVA with one factor currently i'm trying to find the expected value of the mean squares in an ANOVA. However, I think I have a mistake because the latter term is too long and confused me a little. Any help is welcome. ... 0answers 356 views ### The variance of a sum of random vectors There are n vectors each containing exactly q random variables as elements. Each vector is denoted I_k. Each variable within the vector has its own (normal) probability distribution, and the ... 1answer 2k views ### Calculating the standard deviation involving a moment generating function An actuary determines that the claim size for a certain class of accidents is a random variable, X, with moment generation function:$$M_X(t)=\frac{1}{(1-2500t)^4}.$$Calculate the standard deviation ... 1answer 17 views ### Variance - particular outcomes of X If x_i is a particular outcome of the random variable X, and \mu is the mean of the distribution of X, then is it true that E[(x_i-\mu)^2] = Var(X)? Maybe I should ask a different question: ... 1answer 4k views ### Finding the expectation and variance from a probability generating function I need some help with the following question. I managed to get the p.g.f., and can get the expectation and variance in the normal ways, but need a helping hand in deducing them through the use of the ... 2answers 3k views ### How does Variance become an Autocorrelation Function? "For a Gaussian stochastic process X=\{X(t)|-\infty<t<\infty\} with mean function \mu(t)=0 for all t, its autocorrelation function is$$ E(X(t)\cdot X(s))=R(h)=\max(0,1-|h|), h=t-s. $$... 2answers 291 views ### N is a Poisson distribution with mean 4. Find \operatorname{Var}(N\mid N \geq 4) You are given that N has Poisson distribution with mean 4. Find \operatorname{Var}(N\mid N \geq 4) I tried to use the definition of variance, where \operatorname{Var}(X) = E(X^2) - E(X)^2 ... 0answers 162 views ### Monte Carlo integration and variance With the monte carlo integration of a function f(x), what do they mean with the variance? Is it the variance of the function we want to integrate? I = ∫^{\inf}_{inf} f(x)p(x) dx (with p(x) some ... 1answer 21 views ### Simple variance question: variance of the whole expression when one variable is random A very simple question about the variance! I'm interested in the variance of an expression with a random variable inside it. For an expression of this form: a = \sum_{i=1}^{m}(x_i \cdot y_i - z_i)... 2answers 279 views ### Variance of random walk model? I'm taking my second term of statistics, and I find myself obsessed with an unnecessary detail...again. As follows:$$Y_t=\rho Y_{t-1}+u_t$$That is to say, we are working with a time series. We ... 1answer 164 views ### How do you find variance? Let \{X_n\} be a sequence of independent identically distributed random variables with mean \mu and finite variance.$$T_n= \binom{n}{2}^{-1} \sum_{1\leq i< j\leq n} {X_{i}X_{j}} $$I have ... 1answer 3k views ### Variance of a normal distribution for coin toss. I have difficulties constructing the normal distribution for (20) coin tosses. (Don't ask why, but I never had probability in school.) What is the probability of getting at most 12 heads out of 20 ... 1answer 213 views ### Mean of the deviations from the mean I ve been struggling to understand the below problem.If I could get help with this problem, it would be greatly appreciated. Consider the data y, y+a, y+2a,….,y+na and the deviations of these ... 2answers 29 views ### Three random variables equation Given the random variables X,Y,Z have the same distribution and fulfil the following equalities:$$Var(X+Y+Z)=21,Cov(X,Y)=Cov(Y,Z)=Cov(Z,X)=1$$Find VarX and Var(X+Y). I am lost with this ... 3answers 538 views ### The relationship between sample variance and proportion variance? I'm trying to see the relationship between the sample variance equation \sum(X_i- \bar X)^2/(n-1) and the variance estimate, \bar X(1-\bar X), in case of binary samples. I wonder if the ... 1answer 79 views ### Calculate the variance and expectection of \hat{y} in a linear regression model I have the following linear regression model$$y = \beta_0 + \beta_1 \cdot 40$$where$\beta_0 = 11.1317$,$\beta_1 = 1.01$, and$40$is simply the value of the predictor variable (I guess). As you ... 2answers 77 views ### Finding Expectation and Variance of$X_1$and$X_2$Let$X_1$and$X_2$be random variables such that$E(X_i)=μ_i$and$Var(X_i)=α_i^2$. A. Find$E(X_1+X_2)$and$E(X_1-X_2)$in terms of the μ's and α's. B. Suppose that$E(X_1X_2)=α$. Find$Var(X_1+X_2)...
Here is a picture of my problem Basically, given that $R_X(t) = \log(M_X(t))$, I need to show that $\text{Var}(X) = R′′(0)$. As an attempt, I know that $\text{Var}[X] = E[X^2] - (E[X])^2$ and that \$...