Tagged Questions

0
votes
0answers
113 views

Let X1,X2,…,Xn be i.i.d. N(θ1, θ2), please prove that E[(x1-θ1)^4] = 3θ2^2

If x$_{1}$, x$_{2}$,...,x$_{n}$ is sampled from N($\theta$$_{1}$, $\theta$$_{2}$), how can I prove that E [(x$_{1}$ - $\theta$$_{1}$)$^{4}$] = 3$\theta$$_{2}$$^{2}$? I started off this question ...
7
votes
2answers
350 views

Estimating parameters of a normal distribution: median instead of mean?

The common approach for estimating the parameters of a normal distribution is to use the mean and the sample standard deviation / variance. However, if there are some outliers, the median and the ...
3
votes
0answers
254 views

Is this an unbiased estimator for standard deviation of normal distribution?

Suppose we have $n$ samples, with mean $\mu$. Calculate the average absolute distance from $\mu$, i.e., $$ y = \frac{1}{n} \sum_{i=1}^n |X_i - \mu| \>. $$ Then, take as an estimate of the ...
0
votes
0answers
129 views

Parameter estimation from a Normal distribution

Please can you check if am I correct? I have a random variable $X$ normally distributed with mean $\mu$ and variance $\sigma^2$. I generate two independent sample $T_1$ and $T_2$ with $T_1 < T_2$ ...
2
votes
1answer
229 views

Combining two unequal normal distributions

Let $X_1$ and $X_2$ be independent, normal distributed random variables with equal mean $\mu$ but non-equal standard deviations $\sigma_1$ and $\sigma_2$. Suppose I know $\sigma_1$ and $\sigma_2$ and ...
3
votes
2answers
822 views

When estimating variance, why do unbiased estimators divide by n-1 yet maximum likelihood estimates divide by n?

I am totally confused: On the one hand you can read all kinds of explanations why you have to divide by n-1 to get an unbiased estimator for the (unknown) population variance (degrees of freedom, not ...