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.

1,265 questions
Filter by
Sorted by
Tagged with
37 views

Example value assignments for a discrete random variable X such that E(X) = 1 and Var(X) = 1

I need to define random variables such that their E(X) = 1 and Var(X) = 1 and these values need to be non-negative. So far, the only assignment of values to a random variable that I can think of that ...
20 views

Taylor Series and Multivariate Delta Method

I'm trying to understand delta method for matrices and vectors to find the variance-covariance matrices for the functions of matrices and vectors. Please see my attempt below. I'm not sure it is right ...
17 views

17 views

Help with a variance proof

I've been doing these exercises, but there is a proof (considering a binomial distribution of $n=4$, where $p$ is the probability of something happening, that has a median $m=4p$, prove, using the ...
38 views

Basic Chi square problem

How do I calculate $P(S^2 > 1.8307(\mathrm{PopVariance}))$ if $n =11$? I think I should use the Chi square formula: $$X^2 = \frac{(n-1)s^2}{\mathrm{PopVariance}}$$ But I can't really understand ...
31 views

How can $\sigma^2$ be derived as a function of $\mu$ in a Gaussian pdf?

I have a Gaussian pdf defined as $$f_X(x) =\frac{1}{\sigma\sqrt{2\pi}}\exp\left\{-\frac{(x-\mu)^2}{2\sigma^2}\right\}$$ whose $\mu = \frac{d^2}{6D}$, where $d$ is distance parameter and $D$ is the ...
17 views

Dimensional properties derived from PCA eigenvectors

Background Let's assume I'm using principal component analysis to carry out clustering of a 2-d data set, using a non-normalized covariance matrix to carry out the operation. I then solve for the ...
29 views

How to calculate variance or diversity index in this chart

The bar shows an information regarding a team, in which 5 people know java, 10 know javascript etc How can I calculate diversity in this team, or perhaps the variance if in this case variance is same ...
37 views

Are the mean and variance of a set equals the sum of its means and variaces

I'm not so fit in statistics and I found some controverse answers on the internet so I'm asking here. I have a set $A$ with 10439 samples. The set is not of unique values and many of the sample ...
21 views

What is the probability mass function of the measured voltage?

In a specific design, the true voltage of a circuit is 250 millivolt(mV). Measurement error that is continuous and uniformly distributed from -3 to +3 mV is added to the true voltage. the measurement ...
46 views

49 views

Finding variance without the data

A researcher is testing the effectiveness of a political video. She has randomly sampled 120 people to test the video. For each person, there is 50% chance the person will be Democrat and 50% chance ...
31 views

41 views

Variance of double integral of changing error

I have the following case and would like to know if there is a better approach than the one I am currently following. I have an array of errors ($\epsilon(i)$) and an array of corresponding variances ...
25 views

Conditional Expectation of a Sum of Random Variables and a Random Integer

Let $(X_n : n \in \Bbb N)$ be a sequence of identically distributed random variables, with mean $\mu$ and variance $\sigma^2 < \infty$. Set $S_0 = 0$ and $S_n=X_1+X_2+...+X_n$ for $n>0$. Let $N$...
27 views

What is the minimum variance band of Poisson Distribution?

I am trying to calculate the minimum variance bound of Poisson Distribution. poisson distribution: P(X=x)=(λ^x)/x! e^-λ, were λ is the mean. I got λ/(sum of x), but I am not sure if this is right. ...
30 views

How to show that the error variance of the best linear predictor is inferior to the proportional predictor?

Let's consider the 1D case. How do we prove that the error variance of the Best Linear Predictor (BLP) is inferior than the Proportional Predictor (i.e. the Linear Predictor without the intercept)? ...
90 views

I have a question about the problem mentioned above, the main says $X$ Has distribution $U(0,1)$ and $Y$ has distribution $U(0,X)$ Find $E(Y)$ and $Var(Y)$ I try to take it for $E[Y|X]=X$ and $... 4answers 2k views Variance of sine and cosine of a random variable Suppose$X$is a random variable drawn from a normal distribution with mean$E$and variance$V$. How could I calculate variance of$\sin(X)$and$\cos(X)$? (I thought the question was simple and ... 0answers 88 views Show that T achieves the Cramer Rao lower bound Problem Statement: Consider$T$to be an estimator of$\theta$. Show that$T$achieves the Cramer Rao lower bound if and only if$Z$is a linear function of$TZ=a(\theta)T+b(\theta)$... 1answer 123 views We have an urn with 6 red balls and 4 green balls. We have an urn with 6 red balls and 4 green balls. We draw balls from the urn one by one without replacement, noting the order of the colors, until the urn is empty. Let X be the number of red balls ... 1answer 14 views $Y = \frac { K A ^ { 3 } } { ( B + D ) ( C - D ) }$K is a constant Find an expression to approximately determine the variance of Y, assuming$A , B , C ,$and$D$are probabilistically independent. isnt the expression they have already given me the ... 1answer 46 views Minimum variance of$k_1X+k_2Y$where$X,Y$are independent Poisson I have the following question for homework: Suppose that$X$and$Y$are independent Poisson distributed values with means$\theta$and$2\theta$, respectively. Consider the combined estimator ... 2answers 204 views Variance and mean of balls in bins limited capacity Let there be$m$indistinguishable balls,$k$bins,$C$capacity. Let$X_j$denote the total balls in bin$j$. I've seen ways to calculate the total number of combinations, but I'm not sure how to go ... 2answers 26 views A random variable$X$is number of boys out of$n$children. Calculate$\operatorname{Var}(2X-n)$Let a random variable$X$be the number of boys out of$n$children. The probability to have a boy or a girl is$0.5$. Calculate$V(2X-n)$. I know that$Var(2X-n)=4V(X)$.$\mathbb{P}(X=k)={1\over 2^...
Let's say I have a data set of $10,20,30$. My mean and variance here are mean= $20$ and variance = $66.667$. Is there a formula that lets me calculate the new variance value if I was to remove $10$ ...