# normal-distribution's questions - English 1answer

3.282 normal-distribution questions.

### Maximum likelihood estimate for a univariate gaussian

Say we have a univariate Gaussian distribution $p(x)=\mathcal N(x|\mu, \sigma^{2})$. Then suppose we have a data set of observations $X = \{x_1, x_2, \cdots ,x_N\}^{T}$ that are drawn independently ...

### Joint distribution of least square estimates $(\hat\alpha,\hat\beta)$ in a simple linear regression model

Let $Y_1,Y_2,\cdots,Y_n$ be independently distributed random variables such that $Y_i\sim\mathcal N(\alpha+\beta x_i,\sigma^2)$ for all $i=1,\cdots,n$. If $\hat\alpha$ and $\hat\beta$ be the least ...

### Student t - critical value [duplicate]

i need critical value for $t_{249}(0,975)$. I can generate in R in easy way, but in school we will have just tables and in tables are only critical values for degrees of freedom = 100,200,500. How ...

### Proof of process converges to standard Wiener process

I am studying associated variables for applying them on some proofs of GARCH(1,1). I found a paper of Newman and Wright (1981), where a formula which I need is given in a theorem. I need help at the ...

### -1 Find $X, Y$ such that $X+Y$ is standard normal with proof [on hold]

I know that two normal distributions when added will give a normal distribution, and through this I can arrive at the standard normal. However, I need to prove $X$ and $Y$ give a standard normal $Z$ ...

### 4 What is inverse CDF Normal Distribution Formula

1 answers, 4.428 views normal-distribution inverse-cdf
Do anyone know what is Inverse Cumulative Distribution Function of Normal Distribution formula or equation? I am looking at Google but did not find any good answer.

### Sample size required to establish the significance of shift in the mean

I was reading a research paper about climate change and in it the authors say that, in order to establish the significance of a shift in the mean of a standard normal distribution at the $5\%$ ...

### 1 Statistical tests, when data are not normally distributed & variance is not equal

I have a data with two variables - one variable is quantitative, and one is nominal (4 categories). I ran the normality tests and it turned out that this quantitative variable is not normally ...

### Bivariate Normal Distribution with correlation and mean [migrated]

0 answers, 19 views r normal-distribution bivariate
How can I generate k bivariate normal random variables with mean=0 sigma=1 and correlation=rho in R?

### 1 Mixing distributions of 2 RVs: Do we add densities or CDFs?

1 answers, 10 views distributions normal-distribution
I've been solving this book "40 puzzles and problems in probability and mathematical statistics" and I came across this question of mixing RVs vs. mixing distributions. Consider a RV, B, that comes, ...