# Tagged Questions

16 views

### Multivariate student t distribution as a mixture of distribution

I would like to derive the likelihood function corresponding to a student t model as a mixture of distribution, but there is one point which is not completely clear to me. It is usually written that ...
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134 views

### Mean and variance of inverse of a normal RV

My random variable $X$ is normally distributed with mean $b$ and variance $p$. I defined a new RV, $Y$, such that $Y=1/X$. Does anyone know how to find the mean of $Y$ and $Y^2$?
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For bivariate zero-mean normal distribution $P(x_1,x_2)$, the quadrant probability is defined as $P(x_1>0,x_2>0)$ or $P(x_1<0,x_2<0)$ and according to ...
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### Hypothesis testing of normal distributions when mean and range on variance is known

Hypothesis testing problem: $H_0: y \sim N(m_1,v_1)$ $H_1: y \sim N(m_2,v_2)$ . The means $m_1, m_2$ are known and variances $v_1, v_2$ are unknown but upper and lower bounds on $v_1, v_2$ are ...
124 views

### Kullback-Leibler divergence of two normal distributions

I was recently trying to find a way to compute the KL-divergence between 2 populations that are normally distributed using the mean and variance of each population. But I found several different ...
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2k views

### Bottom to top explanation of the Mahalanobis distance?

I'm studying pattern recognition and statistics and almost every book I open on the subject I bump into the concept of Mahalanobis distance. The books give sort of intuitive explanations, but still ...
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### Proof of a PD covariance matrix for conditional Gaussian

I was looking at the formula for the conditional covariance of a partitioned matrix. I understand the intuition behind the equation for the conditional covariance, but I'm not sure how to show that ...
137 views

### How to show that $E[(\hat\theta -\theta)^2]<Var(\bar X)=\dfrac{1}{n}$?

Suppose $X_1, X_2, \dots, X_n$ are i.i.d $N(\theta, 1),\theta_0 \le \theta \le \theta_1$, where $\theta_0 \lt \theta_1$ are two specified numbers. Find the MLE of $\theta$ and show that it is ...
75 views

### how to calculate E[vech(x x')vech(x x')']?

Supposing a vector x follows normal distribution. I want to calculate the expectation of the "fourth moment" in a vector form, meaning $\text{E}[\text{vech}(x x')\text{vech}(x x')']$, given that we ...
I have a random variable $X(a) = \log(a)$ where a is normal distributed $\mathcal N(\mu,\sigma^2)$. What can I say about $E(X)$ and $Var(X)$? An approximation would be helpful too.