# Tagged Questions

In probability, conditional probability, is the probability that an event occurs given something else has already occurred.

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### Determine the probability distribution of a ratio of two random variables?

Setting You are given two independent random variables $X_0,X_1$ with common exponential density $f(x) = \alpha e^{-\alpha x}$. Let $R = \frac{X_o}{X_1}$. Determine $\Pr[R > t]$ for $t > 0$. I ...
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### Conditional expectation for exponential random variables

A man puts his house for sale, and decides to accept the first offer that exceeds the reserve price of $£r$. Let $X_1,X_2,...$ represent the sequence of offers received, and suppose that the $X_i$ are ...
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### Conditional Expectation on Bernoulli Variables

From Basic Probability Theory by Ash: Let $R$ be the number of successes in $n$ Bernoulli trials, with probability $p$ of success on a given trial. Find the conditional expectation of $R$ given that ...
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### Check my reasoning on three conditional probability problems?

Please remember that I am supposed to use conditional probability!! First problem: S is a set of permutations of (1, 2, 3, 4, 5, and 6). The first term of the permutations cannot be 1. If we ...
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### Given that two people were at a location at the same time, find the probability they were there at a particular time

Roger and Stacy each go to the county fair on the same day. They each separately show up at a random time between $12:00$ PM and $9:00$ PM. Roger stays for $2$ hours and Stacy stays for $3$ hours. ...
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### conditional probability question - Sanjay the kindergartener with chicken pox

Suppose the following facts to be true: -- The probability of a random kindergartener having chicken pox at any given time is 2%. -- Among kindergarteners who have chicken pox, 75% have red spots. ...
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### Proof of Independence of two functions of random variables

If we have two random variables $X$ and $Y$ ($0<x<y$) and we know the conditional density $f(x\mid y) = \frac{3x^2}{y^3}$, how can we show that $Z = \frac{X}{Y}$ and $Y$ are independent? ...
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### Probability with qualifications and gender

Qualification Female Male Degree 5 1 None 5 4 School 8 12 Vocation 8 7 I've been going through some ...
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### Given the joint pdf $f_{X,Y}(x,y) = 2e^{-(x+y)}$, $0 \leq x \leq y$, $y\geq 0$. . Find $P(Y < 1| X = 1)$.

Given the joint pdf $f_{X,Y}(x,y) = 2e^{-(x+y)}$, $0 \leq x \leq y$, $y\geq 0$. . Find $P(Y < 1| X = 1)$. Attempt: $P(Y < 1| X = 1) \frac{P(Y<1, X = 1)}{P(X = 1)}$ Can someone please ...
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### Two methods for the Nash equilibrium give different answers; which is correct?

Suppose we have a game, played in which Alice and Bob play mixed strategies: (Sorry about the spacing, but I don't know how to put a table or tab spacing in this text box.) Alice plays Dove with ...
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### Basic Conditional Probability Question - Please Check My Working

Messages relating to the status of an industrial system are transmitted to a monitoring station via an internal transmission network. During periods of low network traffic, 1.2% of these messages have ...
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Messages relating to the status of an industrial system are transmitted to a monitoring station via an internal transmission network. During periods of low network traffic, 1.2% of these messages have ...
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### How should I approach this Conditional Probability Problem?

Can anyone give a hint on how to begin this problem? Suppose $Y = X^2 + W$ where $W$ is Gaussian $N(0, 1)$ noise. Then derive an expression for $P(Y\mid X)$. I know about Bayes' Rule but I'm not ...
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### Gaussian processes versus Bayes rule misinterpretation

I would like to use Gaussian processes (GP) for Bayesian classification of medical data. I think I already understand the basic stuff but I have some uncertainties that are perhaps partly related to ...
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### Inverse Probability and conditional probability.

An unbalanced die (with 6 faces, numbered from 1 to 6) is thrown. The probability that the face value is odd is 90% of the probability that the face value is even. The probability of getting any even ...
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### Problems relating conditional probability [closed]

We choose two numbers from the set $\{1,2,\dots,100\}$. Say the smaller number is $\leq20$. What is the probability of the second number being $\geq80$?
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### Conditional Distribution: how to set up Limit of Integration of a joint density

I have a question in conditional probability. I'm asked to find the conditional distribution, however, I'm unsure about the answer given and would appreciate someone helping straighten out the theory ...
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### Support of the conditional distribution of a poisson process

I am working on Problem 5.1.8 of this book. It states: Let $\left\{X(t),t \geq 0 \right\}$ be a Poisson process of rate $\lambda$. For $s,t >0$, determine the conditional distribution of ...