# Tagged Questions

69 views

### Finding the mean of a Gaussian distributed random variable given the variance

I have a Gaussian distributed random variable $X$ with known variance $\sigma^2$. Given that I know $P(X\geq t)=m$, how can I find the mean of the random variable?
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### Is the mean of n independent Bernoulli random variables normal? [duplicate]

I'm trying to figure out the difference between an A/B split test and an ANOVA test and I came across this article. It suggests that the mean of $n$ independent Bernoulli random variables is normally ...
84 views

### Finding the expected value of two normal random variables

Suppose $a_1 = b + c_1$ and $a_2 = 2b + c_2$ where $b, c_1, c_2$ are all $N(0,1)$ Find $E[b|a_1,a_2]$ My attempt: As $E[b] = 0$, I assume $E[b|a_1, a_2] = 0$. Is this a logical assumption?
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### Do we have an equation to calculate harmonic average using arithmetic average and standard deviation as input?

I would like to calculate a harmonic average of a normal distribution using the mean and the standard deviation using an equation.
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### Simple homework question about normally distributed variables

The question states: Consider a set of random variables $X_i$, where $i=1,...n$. Each $X_i$ is normally distributed with mean $0$ and variance $1$, i.e. $X_i$ are $\mathcal N(0,1)$. What is ...
170 views

### Mean of a function of $K$ Gaussian random variables

Consider $K$ Gaussian random variables $Z_1, Z_2,\ldots,Z_K$ that are mutually independent with $Z_1 \sim \mathcal{N}(\mu,\sigma^2)$ and the remaining random variables $\sim \mathcal{N}(0,\sigma^2)$. ...
498 views

### Maximum likelihood of function of the mean on a restricted parameter space

I've been trying to teach myself some of the fundamentals of statistics by trying to work through old qualifying exams. Here's a problem: Suppose $X_1, \ldots, X_n$ are a random sample from a normal ...
230 views

### Confusion regarding the confidence interval

I have some confusion regarding confidence interval. I was going through this link http://www.stat.yale.edu/Courses/1997-98/101/confint.htm It has something like this: Suppose a student ...
316 views

### Average of a tail of a normal distribution

I have a sample that is pretty normally distributed with a mean greater 0. Is there any way to get a closed form estimate for the mean of all values that are less than 0? In other words, given a mean, ...
34 views

### Improving an estimate of mean with observations of sign

Suppose $x_i$ are drawn i.i.d. from a $p$-variate Gaussian, $\mathcal{N}\left(\mu,\Sigma\right)$. Suppose one observes $x_1,x_2,\ldots,x_n$. One also observes $s_{n+1},s_{n+2},\ldots,s_{n+m},$ where ...
336 views

### Mean and standard deviation of Gaussian Distribution

I have some random numbers which are generated from Gaussian Distribution. But I don't know the mean, standard deviation of that distribution. How can I find them using random numbers?
3k views

### How to compute the confidence interval of the ratio of two normal means

I want to derive the limits for the $100(1-\alpha)\%$ confidence interval for the ratio of two means. Suppose, $X_1 \sim N(\theta_1, \sigma^2)$ and $X_2 \sim N(\theta_2, \sigma^2)$ being independent, ...
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### Mean and variance of a normally distributed random number created from the average of a set of uniformly distributed random numbers

An old-fashioned way of generating normally distributed random numbers entailed setting each normally distributed random number equal to the average of a set of uniformly distributed random numbers, ...
Let $Z=(X+Y)/2$, where $X$ and $Y$ are independent normally-distributed random variables with known variances $\sigma^2_X$ and $\sigma^2_Y$ and unknown (and possibly different) means. Given a sample ...