11 questions linked to/from Identity of moment-generating functions
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if 2 random variables have exactly same mean and variance [duplicate]

If two continuous random variables have exactly the same expected value and variance, do they always have the same distribution?
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How is the kurtosis of a distribution related to the geometry of the density function?

The kurtosis is to measure the peakedness and flatness of a distribution. The density function of the distribution, if it exists, can be viewed as a curve, and has geometric features (such as ...
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Whether distributions with the same moments are identical

Following are similar to but different from previous posts here and here Given two distributions which admit moments of all orders, if all the moments of two distributions are the same, then are they ...
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How would you explain Moment Generating Function(MGF) in layman's terms?

What is a Moment Generating Function (MGF)? Can you explain it in layman's terms and along with a simple & easy example? Please, limit using formal math notations as far as possible.
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How to fit an approximate PDF (i.e.: density estimation) using the first k (empirical) moments?

I have a situation where I am able to estimate (the first) $k$ moments of a data-set, and would like to use it to produce an estimation of the density function. I already came across the Pearson ...
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What is the famous data set that looks totally different but has similar summary stats?

There is a famous example of a collection of datasets with similar summary statistics like mean, standard deviation etc., whose visual appearances are totally different. It is named after the famous ...
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Moment Generating Function for Lognormal Random Variable

I'm working through the proof of a lognormal random variable and am having some difficulty in moving through it. I understand the following: Our CDF is $\Phi(\frac{logx - \mu}{\sigma})$, and thus our ...
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Estimate probability of event using moments of a distribution or a Taylor expansion involving the moments

Let's say we have four moments $(\mu_1, \mu_2, \mu_3, \mu_4)$ of a probabilty distribution of a random variable $X$ and the goal is to get the probability $\rm{P}(X \leq t)$ for a certain value of $t$....
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median and mean of the sample mean of i.i.d. log-normal

Let $y:=\frac1n\sum_{i=1}^n x_i$, where $\{x_i\}_{i=1}^n$ is a set of i.i.d. random variables, and every $x_i$ has a lognormal distribution $x_i \sim\text{Lognormal}(\mu,\sigma^2)$. Let $\text{Med}[y]$...