# Questions tagged [conditional-probability]

In probability, conditional probability is the probability that an event occurs given another (conditioning) event occurred.

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### Probability of Invalid document in a large data set

I'am auditing a very large data set of documents. A document can be Valid or Invalid. Checking a document is computationally ...
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### Help finding the probability of a pipe being blocked in a system of parallel pipes

There is a system of pipes from one point to another. Pipe A is the start point, and connects left to right to Pipe B, C & D, which are in parallel and connect to the end point. The pipes can flow ...
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### Is showing that $P(A|B) \neq P(A|{B}^c)$ enough to prove that $A$ and $B$ are not independent?

At least intuitively, to me this means that event B happening/not happening affects the probability of event A happening, which may seem enough to show these two events are not independent. But is ...
1 vote
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### For a set of n Exponential iid RV, what is the probability that the maximum exceeds the sum of the others?

My question stems from self-study of question 91 in page 372 of Ross's Introduction to probability models, 12th edition. The answer is given in the textbook but I am trying to understand a specific ...
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### "randomizing" a sequence of random variables

I have a (kind of) follow up question on this question. Let $I \subset \mathbb{R}$ and for any $a \in I$ let $X_a$ be a real-valued random variable on $(\Omega_a, \mathcal{F}_a, \mathbb{P}_a)$. ...
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### If $X$ and $Y$ are conditionally independent given $Z$, and $X$ and $Z$ are conditionally independent given $Y$, are $X,Y,Z$ independent?

Let $X,Y,Z$ be discrete random variables, I'll use $\perp$ to denote independence. Suppose $X\perp Y|Z$ and $X\perp Z|Y$, does this imply any of the following, $X\perp Y$, $X\perp Z$ or $Y\perp Z$?
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### Conditional distribution of one of the two exponential random variables, given one is smaller than the other

Let $X$ be a random variable with exponential distribution with parameter $a$, i.e. $X\sim Exp(a)$. See https://en.wikipedia.org/wiki/Exponential_distribution for the definition of exponential ...
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1 vote
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### Conditioning in Event Language VS Proposition Language

According to this video, one can freely decide to conceptualize probabilities in terms of either event language or proposition language. It states, "the mathematical rules are applied the same ...
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### Find estimates for $\alpha_0$ and $\alpha_1$ and covariancematrix

I have that $$f(x)=\frac{1}{\sqrt{2 \pi}}e^{-\frac{1}{2}x^2}$$ I have the conditional distribution: $$f_{\beta}(y|x)=\frac{1}{\sqrt{2 \pi}}e^{-\frac{1}{2}(y-\beta_0-\beta_1x-\beta_2x^2)^2}$$ and we ...
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### Given a person's age x, population's average life span u, predict life span.

Given a person's age x, population's average life span u, predict how long person can live? e.g. Say x is 6 and u = 76 one would expect life span of 74. But when x is 90, for same u = 76, one would ...
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### How to calculate mean of conditional probability?

If I have $E[(A-B)|C]$ to calculate mean of something, is it equal with $E[A|C]-E[B|C]$? If yes, where I can get the references? Or how to prove it?
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### Probability of finding a specific colored plant in a row.

In a packet of flower seeds 3/4 are yellow flowering and rest are white. If 200 rows of each plants are planted, how many will contain (i) all yellow flowers. (ii) all white flowers (iii) two yellow ...
1 vote
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### Conditional probability (Bayes theorem)

One of the 256 subsets of {1,2,3,4,5,6,7,8} is chosen uniformly at random. Let X be the number of elements of this subset. Let Y be 0 if the subset is empty and be the least element of the subset ...
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### Is the bounded uniform distribution the only continuous parametric bounded distribution with a mean invariant under truncation?

Suppose I have a continuous parametric bounded distribution PDF $f_{a, b}$ with support $[a, b]$. It has mean $$\mu_f({a,b}) = \int_a^b xf_{a,b}(x)dx.$$ We can truncate a distribution to a smaller ...
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