# Questions tagged [probability-distributions]

Questions on using, finding, or otherwise relating to probability distributions, probability density functions (pdfs), cumulative distribution functions (cdfs), or other related functions.

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### A basic doubt on joint distribution

How to calculate the following probability $P(X \leq x, Y=y)$ where $X$ is a continuous random variable and $Y$ is a discrete random variable. I have been given the distribution of $X$ and ...
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### Is there any way to calculate harmonic or geometric mean having probability density function?

I have probability density of function of some data (it's triangular.) How can I calculate harmonic or geometric mean of the data? I know for calculating arithmetic mean of a variable like $K$, I have ...
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### Probability of throwing balls into bins

You are throwing n balls into m bins randomly. What is the probability to be empty of the first $k$ bin? Given $k$ bins are empty. What is the probability to be empty of $(k+1)th$ bin? Forget the ...
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### How is logistic loss and cross-entropy related?

I found that Kullback-Leibler loss, log-loss or cross-entropy is the same loss function. Is the logistic-loss function used in logistic regression equivalent to the cross-entropy function? If yes, can ...
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### Distribution of $\max(X_i)\mid\min(X_i)$ when $X_i$ are i.i.d uniform random variables
If I have $n$ independent, identically distributed uniform $(a,b)$ random variables, why is this true: $$\max(x_i) \mid \min(x_i) \sim \mathrm{Uniform}(\min(x_i),b)$$ I agree that the probability ...