Tagged Questions

The normal, or Gaussian, distribution is a symmetrical bell-shaped curve that is defined by the mean and standard deviation. Parametric statistics tests require the population to be normally distributed. A sample distribution that is normally distributed is used to assume that the population ...

231 views

Finding the z score and p-value of a binomial distribution

Emily is a big fan of lady gaga, and 20% of the songs on her ipod are lady gaga songs. Suppose Emily has her ipod on shuffle and repeat mode, which can be assumed to mean that each song to be played ...
109 views

Why doesn't this represent a normal approximation to the binomial?

Suppose the registrar's office at a college reports 58% of the students live on campus. An intern working in the administration building is unaware of this 58% parameter value. He designs a study in ...
311 views

probability of one random variable being greater than another

Using the normal distribution. Let $X \sim N(1, 2)$ and $Y \sim N(2, 3)$ where $N(\mu, \sigma^2)$ denotes the normal distribution with mean $\mu$ and variance $\sigma^2$. $X$ and $Y$ are independent. ...
69 views

Do we normalize too much? [closed]

Yesterday i read this blog post Predictors, responses and residuals: What really needs to be normally distributed? and I wonder what do you think about it. Personally I totally agree with the ...
55 views

Approximate distribution of normal squared

I am studying for a test, one section of which will cover the delta method. This problem came from that section: Let $X\sim N(\mu,n^{-1})$. Find an approximate distribution of $X^2$. (It also asks ...
98 views

Estimating parameters of a normal distribution from noisy observation of samples

Suppose I have a number of samples drawn from a normal distribution $x_i \sim \mathcal{N}(\mu,C)$ with $i = 1 \dots n$. I can make observations $z_i = x_i + e_i$ for those samples which are perturbed ...
47 views

Plotting a histogram estimate together with an analytical solution of the mean and covariance parameters

How do I plot a histogram estimate of this marginal distribution p(x1): ...
70 views

Is the skew normal distribution log-concave?

Is the skew normal distribution log-concave?
99 views

How can I test the difference between a population proportion and sample proportion?

A report says that 82% of British Columbians over the age of $25$ are high school graduates. A survey of randomly selected residents of a certain city included $1290$ who were over the age of $25$, ...
87 views

231 views

275 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 ...
236 views

How to estimate the parameters of a Gaussian distribution sample with outliers?

I have a sample of length $N$, mostly taken from a Gaussian distribution with unknown mean and variance. Of those $N$ samples, some proportion of them (typically less than 1-2%) are outliers, taken ...
70 views

Can I use RM ANOVA instead of Friedman

I am currently analysing my quantitative data. My sample size is 157 students who sat for a survey in 2 phases after an intervention. The same students sat for the same survey on positive outcomes on ...
112 views

Confusion related to derivation of the log likelihood

I was reading the Hastie, Friedman, Tibshirani paper "Sparse Inverse Covariance Estimation with the Graphical Lasso" and it had the following I couldn't get how the following expression was derived ...
104 views

Sampling from a multivariate normal distribution

When we sample $n$ things from a multivariate normal distribution $N(\mathbf{\mu}, \mathbf{\Sigma})$, does this mean that we choose $n$ vectors of some fixed length $k$? For example, suppose $n=3$ and ...
41 views

Confusion related to derivation of product of gaussian

I am confused. Given how come this is derived?enter image description here
160 views

Distribution of ratio of sample means from two independent normal variables?

The Question We have a sample of size $N$ with mean $\bar{x}$ and SD $\bar{\sigma_x}$ from a random variable $X \sim \mathcal{N} (\mu, \sigma^2)$ We have a sample of size $M$ with mean $\bar{y}$ and ...