All Questions
Tagged with variance probability
232 questions
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X~Unif(0, 1) ; X1 + X2 + ... X6 = 1 ; Y = sum(X1...X6) ; VAR(Y) =?
Let $X_i$ ~ Unif(0, 1) s.t.
$X_1 + X_2 + ... + X_6 = 1$
Let $Y = X_1 + … X_6$
What is $Var(Y)$?
(Also the case when it's $X_n$)
Purpose for the curious:
I'm trying to rank confidence for softmax ...
- 93
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335
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Computing $\mathbb{E}(S_n)$ and $\mathbb{V}(S_n)$ for Bernoulli data with a uniform probability parameter?
Take $U \sim \text{U}(0,1)$ as an underlying probability and generate $X_1,X_2,...,X_n \sim \text{Bern}(U)$ independent Bernoulli trials with this probability. The number of successes in the sample ...
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Does the peak of a Normal Distribution mean anything? [closed]
What does the peak of a Normal distribution show? Let's say if I have a flat peak, does this mean I have a larger variance? What if I have a sharp peak?
For example,
Does the "blue distribution" ...
- 581
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Find standard deviation of arbitrary game with multiple payouts
This earlier question asked how to get a 5.76 standard deviation for a single number bet on Roulette. The answer gave the formula, but unfortunately, the formula doesn't easily generalize to more than ...
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Is the variance of the mean of a set of possibly dependent random variables less than the average of their respective variances? [closed]
Is the variance of the mean of a set of possibly dependent random variables less than or equal to the average of their respective variances?
Mathematically, given random variables $X_1, X_2, ..., X_n$ ...
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central moments of random variable from _estimates_ of draws from the distribution function
I am trying to estimate the first two central moments of random variable $r$. The information I have about $r$ is a set of estimates $\hat{r}_i$ for $i \in \mathcal{I}$, each with corresponding ...
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86
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How to find $\mathbb{E} \left[\frac{\bar{\mu}}{\bar{\sigma}^2}\right]$?
I asked the same question on math stacks: MathStacks:, and some user suggest to ask it here for better insight. So this question has found interest in many research problems, but there have been no ...
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Probability that both the mean and sample variance are both covered by their respective confidence intervals?
I am given the question: "What is the probability that both the mean is in its confidence interval for confidence level a and the variance is in its confidence interval for confidence level a?&...
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Taking derivative of a function containing random variable wrt the variance of that variable [closed]
Say, I have a function containing a random variable such as $ f(X)$, where $X $ is the random variable that comes from a family of random variables that differ only in the first and second moments (e....
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Finding variance from normal distribution
Suppose $Z_1$ and $Z2$ ~$N(0,1)$
Let $X_1=2Z_1$ and $X_2=X_1+\frac{\sqrt{3}}{2}Z_2$
Let $Y_1=\sqrt{3}Z_1+Y_2$ and $Y_2=Z_2$
I understand I have to show the mean and variance for $X_1$ and $X_2$ should ...
- 183
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how do i empirically estimate variance of conditional normal distribution?
I've tried searching for this, but maybe I'm not using the correct search strings. suppose I have joint distribution $P(X_1,X_2)$ over 2 continuous random variables $X_1,X_2$ that I can sample from. ...
- 445
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If $X\in\{0,1\}$, then $\frac{cov(X,Y)}{Var(X)}=\mathbb{E}(Y|X=1)-\mathbb{E}(Y|X=0)$
If $X\in\{0,1\}$, then $\frac{cov(X,Y)}{Var(X)}=\mathbb{E}(Y|X=1)-\mathbb{E}(Y|X=0)$
I have no idea what to address with the conditional expectation part.
Thank you for any comments, someone has ...
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Relative part of Variance
The following problem I have $n$ students who are taking a test in which two items of information $X_1$ and $X_2$ are collected. Now I form another variable $X_3=X_1+X_2$ and want to find out how ...
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130
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Variance of a vector-valued random variable along a unit vector
Let $X$ be a vector-valued random variable with variance $\mathbb{V}[X] < \infty$. How is the variance of $X$ along a unit-vector $\hat{v}$ defined? Can we say that in general it is $\hat{v}^\top \...
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Understanding Covariance after Variance (visually)
2 Points i understood from variance derivation-
A) For calculating Variance we do not subtract (or mod add), but rather sum squared all points' differences from the mean.
B) Variance of 1,2,3 will be ...
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52
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Correlation Based Models vs Covariance Based Models
I am trying to better understand why some models are "covariance based" vs. why some other models are "correlation based".
1) For example, a Multivariate Normal Distribution ...
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145
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Dirichlet distribution parameters from known variances
Let's assume, I know the variances of Dirichlet distribution parameters. Let these variances be:
$Var[X_1], ..., Var[X_n]$.
Is there a analytical solution to derive the parameter value alpha_i given ...
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83
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Law of Total Variance Issue
The Law of Total Variance says:
if the variance of X is finite then $V(X) = E(V(X|Z)) + V(E(X|Z))$
Suppose $X\sim N(0,1)$, $Y\sim \text{Cauchy}(0,1)$, $X$ and $Y$ are independent.
Define $Z \equiv X + ...
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Binomial Distributions Problem
A casino customer bets on red at roulette (probability of success is 9/19). If the result is red, the client is given 3 dollars; but if she loses, she pays 3 dollars. The client plays until she has ...
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Bounds on distance between two independently variables drawn from the same distribution
Suppose $X_1$ and $X_2$ are iid from an arbitrary distribution with variance $\sigma^2$. How can we derive an upper bound for:
$$P(|X_1-X_2|\ge\delta)$$
One simple idea is Chebyshev's Inequality, ...
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Show that if $Y$ is another random variable such that $E[X] = E[Y]$ and $V(X) = V(Y)$ then $P(Y \ge a) \le p$
Let $p \in (0,1)$ and $X$ be a random variable such that $P(X=a) = p, P(X=-b) = 1-p$
Show that if $Y$ is another random variable such that $E[X] = E[Y]$ and $V(X) = V(Y)$ then $P(Y \ge a) \le p$ and ...
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How to calculate variance or standard deviation for product of two normal distributions? [duplicate]
For example if I have two multiplied distributions a * b:
...
- 111
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418
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Get the new variance of the data [duplicate]
I got an initial mean $\mu_1$ and std $\sigma_1$ by sampling samples, these samples are generated by an unknown distribution and later I drop these samples. Then I sampled some samples and got the ...
- 1,391
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Variance of bivariate normal distribution plus normal distribution
Problem:
$W = -27 + 0.3X + 0.45Y + E$
The pair $\begin{bmatrix} X \\ Y \end{bmatrix}$ behaves like a bivariate normal with vector of averages $\begin{bmatrix} 156 \\ 86 \end{bmatrix}$ and ...
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152
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Replacing summation by integral in classical variance of sum formula, is it possible?
It is well known that the variance of the sum of $x_1,...,x_N$ random variables is the sum of their variances plus twice their covariances:
$\text{Var} \displaystyle\sum_{i=1}^{N}x_i =\displaystyle\...
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Expectation and variance of a stochastic time process conditioned on its past
$$dV_t=-k(V_t-1)dt+ \epsilon\sqrt{V_t}dW_t$$
$W_t$ is wiener process and the rest is just some parameters.
For $T_{i+1}>T_{i}$ how do I find the expectation and variance of $V_{T_{i+1}}$ ...
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88
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What are meaningful ways to interpret Monte Carlo-simulated non-normal data?
My question relates to Confidence Interval (CI) calculation of Monte Carlo-simulated non-normal data
As answers and comments to that question show the confidence interval for the given distribution ...
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79
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CLT and 2 variables
Okay so there are 2 variables $D_i$ and $V_i$. Now $D= D_1 + D_2 + ... + D_N$ and $V = V_1 +.. +V_N$
Now I know the relationship is such that $E[D_i - a*V_i] = 0$ and
$Var[D_i - a*V_i] = E[D_i]$ ...
- 489
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Time-partitions of sample size
I am struggling with explain something I read in a Whitepaper. The essence is as follows.
Let's begin with a random variable $X$ defined as number of events in an hours. Further, we assume that $X \...
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Mean and variance of call center data
I have a fairly involved homework question, I was wondering if I could get some help.
There are two types of phone calls arriving at a switch, long-duration and short-duration. Each day the number of ...
- 133
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2
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4k
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Theoretical expected value and variance
Let $X$ be a random variable having expected value $\mu$ and variance $\sigma^2$. Find the Expected Value and Variance of $Y = \frac{X−\mu}{\sigma}$.
I would like to show some progress I've made so ...
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Expresion for Var(X/Y)
I am suggested the following formula and I can't find some reference on this expression :
$$\text{Va}r(X/Y)=E(X^2/Y^2)-E^2(X/Y)=\text{Cov}(X^2，1/Y^2)+E(X^2)E(1/Y^2)-(\text{Cov}(X,1/Y)+E(X)E(1/Y))^2$$
...
user226073
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Standard deviation of discrete variable
A start-up looking to get into the sleeveless shirt market is looking for \$10,000 from investors to get their company started. If you choose to invest this \$10,000, at the end of 5 years the company ...
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1
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How I can calculate in R expected value and variance of X and how do I get the probability? [closed]
In a survey I collected the following data comparing people who prefer to buy coffee or tea:
75% coffee
25% tea
I am assuming that 75% of all people prefer coffee.
On any given day 8 people bought ...
0
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1
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22
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How the variance of a potential loss X has been derived
I'm studying Insurance and I have a question about how the variance has been computed in this example.
Imagine a case where an "agent" may suffer a loss, because of an event (an accident) occurring ...
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588
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Conditional variance of a random variable conditioned on its own value
Suppose that $X$ is a random variable. Does it hold that $\mathbb{V}ar[X|X]=0$? What is the proof/intuition behind this?
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Finding mean and variance of number of tosses needed to get exactly 2 heads
A coin with probability of getting head $0.6$ is tossed repeatedly till two heads appear. Let $X$ be the number of tosses needed to get exactly 2 heads. Describe the sample space. Find the mean and ...
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How is the true label 'constant' in the derivation of the bias-variance decomposition
In the derivation of the bias variance decomposition for example on Wikipedia or in this question the following identity is used:
$$E[(E[\hat{f}]-\hat{f})(f-E[\hat{f}])]=E[E[\hat{f}]-\hat{f}](f-E[\hat{...
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1
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466
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Find variance of an estimator
Let X1,X2..,Xn a random sample from a population X having distribution function
$f(x;θ) = θx^{θ - 1}$ if 0 < x < 1
Where θ > 0 is a parameter. Is the estimator $θ = \frac{x̄}{1 - x̄}$ of θ ...
- 217
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116
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The expected value and variance of E(-1X)? [closed]
This might be a stupid question, but how I can calculate the expected value $\operatorname{E}(-1X)$ and variance $\operatorname{Var}(-1X)$ for example in a case in which $X\sim N(100,0.1^2)$?
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Obtaining Negative Variance. What is the error?
Suppose a dice is thrown $8$ times and success is considered as obtaining either a $5$ or $6$. What is the variance of the number of successes?
Attempt: Let the indicator variable $X_i$ be $1$ when ...
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70
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Compute Conditional Variance
Let the joint density $ f_{X,Y}(x,y)=\begin{cases} c(x^3+2xy),\ 0\le x,y\le 2\\
0, \text{ else}\end{cases}$
be given. I want to compute $Var(Y|X=1)=\int^\infty_{-\infty} (y-E(Y|X=1))^2f_{Y|X=1}(y)\,\...
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37
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Expressing as a probability density function [closed]
The measuring error x is a normal random variable. Variance of the error = 4. If distribution of x can be shown by a probability density function f(x), how would you find the analytical expression of ...
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275
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How to estimate the mean and variance of a Gaussian distribution variable? [closed]
I have two variables 2X and 0.5Y, both are independent and follows Gaussian distribution. How to estimate their mean and variance analytically? I want to know their individual mean and variance, then ...
0
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1
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133
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Variance of linear combination of Normal distributions
A company that develops software received an order for a service to be performed within a week and, in order to decide on the profile of the team of programmers to be used, it should take into account ...
- 107
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1
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93
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Probability - expected value
The random variable $X$ takes on values -2, 0 and 2 with probabilities 1/4, 1/2 and 1/4 respectively. Find $\text{E}(X)$ and $\text{Var}(X)$.
Till this part, it was easy enough.
Then the question ...
user218970
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1
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84
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Largest variance
Let S be the number of successes in n independent Bernoulli trials, with possibly different probabilities $p_1$ $,...,$ $p_n$ pn on different trials. Show that for fixed $\mu$=E(S), Var(S) is largest ...
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1
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29
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Spread on x-axis around an extremum
I am working on a graph that has Power (Watts) on the x-axis and Frequency (not Hertz here, more like the probability that we consume that much power) on the y-axis.
What I would like to do with it ...
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39
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How to check the Variances between 2 estimators are same or not
Let say I have 2 batches of electric bulb from some manufacturing processes
First batch was run from 10 am to 2 pm (just assume). In this batch total $N_1$ number of bulbs are produced and among them $...
- 405
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0
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29
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Expected value of a decreasing function of two random variables
My question is exactly equal to the question posted at Expected value of decreasing function of random variable versus expected value of random variable with just one extra assumption: the two random ...
- 1