New answers tagged joint-distribution
3
votes
Joint distribution of a random variable and the sample maximum
A fundamental result in order statistics is Theorem 2.4.2 of Balakrishnan & Cohen:
Let $X_1, X_2, \ldots, X_n$ be i.i.id. random variables from a population with cdf $F$ and pdf $f,$ and let $X_{...
- 317k
0
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Joint distribution of $Y$ and $S^2-Y^2$
we know, $$\frac{(n-1)S^2}{\sigma^2} \sim \chi^2_{n-1}$$
$$Y = \sum_{i=1}^{n} b_iX_i$$
notice, this is a linear combination of normal random variables so, this should follow normal distribution with
$$...
- 1
3
votes
Joint and conditional probability with Poisson and Binomial distributions
Simple and short
I started below with some long computation starting from your erroneous $P(X \ge 3, Y \ge 1)$. Trying to make an intuitive interpretation of the end result it made me realize that we ...
- 72k
3
votes
Accepted
Joint and conditional probability with Poisson and Binomial distributions
This problem has its roots on compound Poisson process. The correct way of approaching it is to express the number of boys $X$ in a household as
\begin{align*}
X = D_1 + \cdots + D_N,
\end{align*}
...
- 16.8k
0
votes
Accepted
How come the Bayes Theorem formula results in different probabilities that are verifiable using manual counting?
The first two Python code groups that display either 0.4 or 0.3 are wrong. They do not implement Baye's Theorem. The third group is correct. I was just using Baye's Theorem the wrong way. I wanted to ...
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3
votes
Accepted
Transforming data with a fitted distribution function
I cannot add a comment, so I'm writing it in an answer.
Am I wrong to expect the transformed data to be uniform or could there be something else going wrong?
It is the marginal CDF, which is assumed ...
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