# Tagged Questions

For questions involving random variables uniformly distributed on a subset of a measure space. To be used with [probability] or [probability-theory] tag.

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### Find the limit of the probability of uniform random variable?

Let $X_1 ,X_2 ,X_3 ,…$ be a sequence of i.i.d. uniform $(0,1)$ random variables. Then, calculate the value of $$\lim_{n\to \infty}P(-\ln(1-X_1)-\ln(1-X_2)-\cdots-\ln(1-X_n)\geq n)?$$ My work: Since ...
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### Uniform Distribution / Normal Distribution

Let the random variable X ~ U ( 0, k ) and Y is a second random variable such as Y | X ~ N ( X , 1). a) Determine the Y density function if k = A . b) Determine the value of k if COV [X , Y ] = B. a) ...
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### Why these two distributions are different when I calculated them?

Two insurers provide bids on an insurance policy to a large company. The bids must be between 2000 and 2200 . The company decides to accept the lower bid if the two bids differ by 20 or more. ...
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### Proof Attempt: Non-decreasing continuous CDF is standard uniformly distributed

Proof Attempt: For any random variable $X$ with non-decreasing continuous cdf $F(x)=\Pr(X≤x)$ (note that the inverse function does not necessarily exist due to flat regions in $F$), I wish to prove ...
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### how far the distribution from the uniform distribution

I have two discrete probability distributions $P$ and $Q$, where $P=(p_1,...,p_n)$ and $Q=(q_1,...,q_n)$, in addition I have uniform distribution $U=(\frac{1}{n},...,\frac{1}{n})$. The question is ...
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### Probability involving the maximum of i.i.d. uniform r.v.'s

The question is : $100$ numbers are independently and uniformly distributed on $(0,1)$.Then what is the probability that the maximum of these numbers will be at most $0.9$? How can I solve it? ...
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### estimate a probability

Let $X_1....X_{48}$ be independent random variables, each follows a uniform probability distribution over [0,1]. What is the best way to estimate P($\Sigma_{i=1}^{48} X_i > 20)$?
I struggle to understand the transformation of a random variable with uniform distribution. For example: Let $X\sim \text{Uniform}(0,1)$ and $T=-2\ln(X)$ and I want to find the CDF of $T$, then I ...