# Tagged Questions

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### I have a question on conditional P with multiple events

I'm following this "Modeling and Reasoning with bayesian networks book's problems and Im stuck in this: ...
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### Compute the inverse of function [on hold]

I want to compute and plot the inverse of given function f. I have the following code in R : ...
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### Number of trials needed to increment a counter variable

Truthfully I'm not even sure what the proper name for this sort of trial is, so I'll just describe the whole setup. Suppose I have an integer variable n, which starts at zero and gets incremented ...
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### Probability and Sampling distribution

Would you please explain me the difference between Probability distribution and Sampling distribution easily ? Is that the difference : in probability distribution we have probability for every ...
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### Utility of Probability Generating Function [on hold]

The utility of Probability Generating Function , how far known to me , is basically to generate PMF uniquely (what all the popular books of probability have written ) . Now , PGF is constructed with ...
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### Probability of two outcomes of Geometric distributions (dependent?)

So let an binary experiment yield event, A, with probability p. Let there be a second binary experiment yield event, B, with probability p′. The experiment that yields B can only occur after A has ...
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### Dependence of distribution standard deviation with subtraction of its mode from mean of normal distribution

The following question might have relations to this question: Given $\mu$ and $\sigma$ (mean and standard deviation) of normal distribution, find the set of all distributions with their $\mu_1$ and ...
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### Correlation of distribution standard deviation with subtraction of its mean from mean of normal distribution

The following question might have relations to this question: Given $\mu$ and $\sigma$ (mean and standard deviation) of normal distribution, find the set of all distributions with their $\mu_1$ and ...
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### Expected number of cards drawn

You draw cards from a standard 52-card deck without replacement until you get a queen of spades and stop. The cards have the values $2,3,4,\ldots,11(J),12(Q),13(K),14(A)$. The first card you draw ...
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### I need to check if I'm correct, with conditional and bayes

I have this problem: ...
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### Conditional table, how to fill it

I found this question and since I'm learning probability I'm not sure how to go about it: ...
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### $X$ and $Y$ are independent if and only if $\sigma(X)$ and $\sigma(Y)$ are independent [on hold]

Let $X$ , $Y$ be random variables on probability space $(\Omega , \mathcal B, P)$. show that $X$ and $Y$ are independent if and only if $\sigma(X)$ and $\sigma(Y)$ are independent.
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### Sum of sample mean and sample variance sampling distribution

Let $X_1, X_2, \cdots, X_n$ be an identical and independently distributed sample from $N(\mu, \sigma^2)$, define: $$D = \frac{1}{t}\left[\overline{X} + \frac{1-\rho}{2} S^2\right]$$ where: $t$ and ...
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### Proving basic probability inequalities

So the title is a bit vague, but I am trying to solve some basic probability inequality. Given that $P(B\cap C) > P(B)P(C)$, how can I show that $P(B|C) > P(B|W\setminus C)$? I started by ...
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### Conditional probability problem - acceptance to two colleges

I'm doing this problem: ...
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### Total probability theorem with normal probability density functions

Let $X$ and $Y$ be two continuous random variables. Suppose that: $X$ has normal pdf with mean mu_1 and variance $\sigma_1^2$ $Y|X$ has normal pdf with mean $mu_2=(a+b*X)$ and variance $\sigma_2^2$; ...
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### I have 2 problems with conditional probability, involving coins and dice

Hi I have these problems: ...
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### Probability to get equal cars

A famous car production company produces 3 different models of cars, available in 5 colors and 3 possible CC(1900 cc,2000 cc and 2200 cc). suppose that every combination of model, color and CC has ...
The inequality: $$\Pr(\overline X - \mathrm{E}[\overline X] \geq t) \leq \exp \left( - \frac{2n^2t^2}{\sum_{i=1}^n (b_i - a_i)^2} \right)$$ Is this bound (or any other form of hoeffding) tight in ...