# Questions tagged [probability]

For basic questions about probability and for questions about calculating a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using [tag:measure theory]), ask under [tag:probability-theory] instead. For questions about specific probability distributions, use [tag:probability-distributions] instead.

67,776 questions
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### If Grace and her friends were to roll the two dice 100 times, how many of the 100 times could they expect to roll the same number on each die? [on hold]

need some help on this question I tried the question out but still don't understand
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### What is the base measure in measure theory?

I see the term "base measure" used frequently about measures. I do not completely get what that exactly means: Some examples are: Let $\cal F$ be the space of all probability density functions ...
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### Can a stochastic process be neither adapted to filtration nor previsible?

The idea behind the question arises from my intuition about the concepts of 'adapted to filtration' and 'previsbility'. If a process is adapted, it essentially means that the evolution of the ...
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### Using Markov chain instead of total probability

This question was given to me as a review for an upcoming exam: If a baseball team wins a game, they have a 40% chance of winning the next game due to getting overconfident. If they lose the previous ...
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### Sample two individuals and find the probability of the following events

Blood can be classified according to ABO-type: $A$, $B$, $AB$ and $O$, but also according to Rh-type, $P$ (positive) and $N$ (negative). Suppose that every individual has one Rh-type and one ABO-type ...
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### If $X_n$ and $Y_n$ are independent does $(X_n,Y_n)\overset{d}{\rightarrow}(X,Y)$?

More formally: If $X_n\overset{d}{\rightarrow}X$ and $Y_n\overset{d}{\rightarrow}Y$ and also $X_i$ and $Y_j$ are independent for all i,j; does $(X_n,Y_n)\overset{d}{\rightarrow}(X,Y)$? I am aware of ...
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### Simple probability equality proof [on hold]

For given continuous random variable A,B,C and arbitrary continuous function f, and probability density function p, can you help prove/disprove following equality? p(A, B, f(A,B)) = p(A, B) p(A, B, ...
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### Probability that maximal elements has the same position in samples from correlated random variables

Let $x$ and $y$ be two correlated random variable (say, standard normal) with correlation coefficient $\rho>0$. Let $X= \{x_1, x_2, ..., x_L\}$ and $Y= \{y_1, y_2, .. y_L\}$ be samples of size $L$ ...
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### Analytic proof of area probability

$X,Y$ are i.i.d. $unif(-1,1)$ random variables. Prove that $$P(X^2+Y^2\leq 1)=\frac{π}{4}$$ Geometrically, I understand how that happens. $(X,Y)$ is a random point in square having centre at origin ...
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### Dart board probability using line method with Poisson application

You randomly throw darts at a dartboard, one dart every second. Suppose that every dart independently hits the dartboard at distance X from the center, where X is a Unif[0,30] random variable. Your ...
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### Calculate number of failures until success where the probability changes after a failure.

How do you calculate the expected value of the number of failures until the first success is reached where the probability will change after a failure. Let $p$ be the probability of success. Let $X$ ...
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### Policy gradient base line function

On the bottom of page ten of the following paper on probabilistic reinforcement learning, there are 3 equations where is author manipulates the policy gradient $\nabla_\theta J(\theta)$. Can someone ...
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### The paradox of random occurrence the family problem

we have 100 families: 10 families have no children, 40 families have 1 child for each one, 30 families have 2 children for each one, 10 families have 3 children for each one and 10 families have 4 ...