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.

1,235 questions
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What is the trick in the derivation? Density of a complicated function

Through one of the proofs I found a problem that really cannot solve. Imagine some density function f(x). Now, imagine that the argument is a function of the form x+c(f'(x)/f(x)). Therefore, the ...
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Joint Uniform Distribution SOA question 93

This is a question from SOA: A family buys two policies from the same insurance company. Losses under the two policies are independent and have continuous uniform distributions on the interval from 0 ...
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Chi Squared Distribution with $\mu = 0$, $\sigma^2 \neq 1$

Let $X_i$ be independent normally distributed random variables with zero mean and variance $\sigma^2 \neq 1$. What is the probability density function of the random variable formed by the sum of their ...
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How to model this distribution using Central Limit theorem?

I have distribution that can be defined as below, $S=a_0\cdot b_0 + a_1\cdot b_1 + a_2\cdot b_2 + \cdots +a_{n-1}\cdot b_{n-1}$ Now, I want find the distribution of $S$ when, $a_i$'s are selected ...
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PMF from two discrete probabilities [closed]

If I have two probabilities, $P(X>n)$, and $P(X>n+m)$, how would I go about obtaining a PMF of some random variable $X$? This problem seems simple enough but I am totally lost on how to arrive ...
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What is the smallest number of socks you should pull out so that you can be assured that you will have at least one pair of matching socks? [closed]

Anyone can help me with this math problem? Your drawer has 5 pairs of black socks, 4 pairs of gray socks, 2 pairs of white socks, 1 pair of brown socks, and 1 pair of blue socks. The lights are ...
Question about Markov moment and $\sigma$-algebra [closed]
Let $\tau$ be the Markov moment with respect to the stream $(\mathcal{F}_{t}, t \in T)$. Prove that  \mathcal{F}_{\tau}=\{A \in \mathcal{F}: A \cap \{ \tau \leq t \} \in \mathcal{F}_t, \quad \...
$X$ is a uniformly distributed random variable on $(0,1)$ $Y$ is a uniformly distributed random variable on $(0,2)$ $Z$ is a uniformly distributed random variable on $(0,4)$ What is the probability ...