# Tagged Questions

This tag is for basic questions about probability and for questions in which one wants to calculate a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using measure theory), please ask under (...

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### Inequality for binomial distribution

In a bombing attack there is $50\%$ chance that any bomb will hit the target. Two direct hits are required to destroy the target completely. How many bombs must be dropped to give a $99\%$ chance or ...
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### Tilde notation, what does it mean

A bit of a newbie question, but what exactly does tilde mean in this case? $$P(X>x) ∼ Cx^{−α}$$ This is in a context of some distribution (say Gaussian) that has Paretian tails. I have seen this ...
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### Conf. Interval for a simple mixture of Normals

Imagine there's a prob. p=0.5 of choosing one machine or the other to take some measurements $X$ for an experiment. One machine ($N(\theta,10)$) is much less precise than the other($N(\theta,0.1)$) ...
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### Weighted War - Game of Mind and Probability

Weighted War is a game of bidding, where: Both players have cards valued from $1$ to $11$ in their hands There is a third pile of cards from $1$ to $11$ face down on the table and shuffled,...
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### Query on how the Probability is derived in the below scenario

A large pool of adults earning their first driver’s license includes 50% low-risk drivers,30% moderate-risk drivers, and 20% high-risk drivers. Because these drivers have no prior driving record, an ...
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### Why am I under-counting when calculating the probability of a full house?

I was trying to answer this question. Find the probability of getting a full house from a $52$ card deck. That is, find the probability of picking a pair of cards with the same rank (face value), ...
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### Probability: 5 cards drawn at random from a well-shuffled pack of 52 cards [closed]

A poker hand consists of 5 cards drawn at random from a well-shuffled pack of 52 cards. Then, the probability that a poker hand consists of a pair and a triple of equal face values (for example, 2 ...
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### Problem of joint density function of random variable $(X,Y)$.

The joint density function of $(X,Y)$ is $$f(x,y)=\begin{cases}6(1-x), & 0<y<x,0<x<1\\ 0, & \text{otherwise}\end{cases}$$ Then which of the following are correct? $X$ and $Y$ ...
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### Modified random one dimensional walk problem

If I take one step right from my initial position, I will fall off a cliff. My goal is to get to safety, which is exactly $x$ steps to my left. I decide which direction I will make my next step by ...
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### Explanation of “When two functions $a(x)$ and $b(x)$ are not correlated on domain $X$, they can be separately integrated”

Hy everyone, I was reading this paper https://hal.inria.fr/hal-00942452v1/document , and I came up with a statement that I don't fully understand, nor could I found any info on it, so decided to ask ...
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### PDE boundary condition question regarding limits

Just as a bit of background, I'm working with the Black-Scholes PDE and I'm testing some things out by taking an initial condition for it as $\sin(S/50)$, where $S$ is the spot price (but that's ...
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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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### Asymptotics of $\lim\inf X_n$, missing part of exam question [closed]

So I was working through an old exam and encountered the hilarious situation that part of the statement of the exercise was illegible. I was wondering if anyone could figure it out for me, so that I ...
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### Bound for sum of normal distributions

I have encountered an exercise that was quite puzzling for me. Maybe someone can help me out here? So let $(X_n)_n$ be $N(-a,1)$ distributed, independent random variables where $a>0$. I need to ...
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### Maximum-a-posteriori estimation with Gamma prior and scale-invariant likelihood

Let $\mathbf{X}$ be a vector of parameters with prior distribution $X_i \sim \text{Gamma}(\alpha, \beta)$ i.i.d. for $i = 1, \ldots, n$. Let us denote this prior by $p(\mathbf{X})$. We get to observe ...
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### What is the distribution of the square of a sum of correlated Gaussian random variables?

Suppose a random vector $X\in\mathbb{R}^n$ follows a centered multivariate Gaussian distribution with zero mean and covariance $\Sigma$. We know that a linear combination of every elements in $X$ ...
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### How to convert this text into probabilities?

How do we convert the table into probabilities? Let $S=\text{patient survives}$, $J=\text{patient is junior}$, $Sr=\text{patient is senior}$. Can we say that $P(S|J,T_2)=0.5$, or $P(S|Sr,T_2)=0.35$? ...
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### Implications of conditional independence

Suppose two $\sigma$-algebra's $\mathcal{F}_1,\mathcal{F}_2$ are conditionally independent given some $\sigma$-algebra $\mathcal{G}$ i.e. for any $A\in \mathcal{F}_1$, and $B\in\mathcal{F}_2$, we have ...
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### Calculating probability of winning best-of-7-games tournament. Why is my method wrong?

The question is as follows: A and B participate in a tournament of "best of 7 games". It is equally likely that either A wins the game or B wins the game, or the game ends in a draw. What is the ...
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### Question from probability [closed]

10 students appeared for two examinations. 6 students passed the first exam, 5 students passed the second exam, and 3 students passed both the first and the second exam. What is the probability that ...
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### One Independent Trial, What is the Chance of One Result Occurring First?

Each trial can result in one of three possible results. Result A happens 50% of the time. Result B happens 30% of the time. Result C happens 20% of the time. Each trial is independent. I want to ...
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### Convolution mixture of a probability generating function (population genetics)

I'm trying to work through an old population genetics paper (see here). The following model assumes an infinite number of nucleotide sites and no recombination between different sequences (so you can ...
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### Conditional expectation of a product of random variables

I have two independent continuous random variables $X$ and $Y$ with pdf's : $f(x)$ and $f(y)$ cdf's : $F(x)$ and $F(y)$ a constant $a$ I am trying to express using the given pdf/cdf functions the ...
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### How to adjust estimation of probability according to new information

Suppose $\{a_1,a_2,\dots,a_n\}$ is a permutation of $\{1,2,\dots,n\}$. The probability of $a_i=j$ is estimated to be $p_{ij}$. The probability matrix might look like this  P=\left( \begin{matrix} ...
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### Four people are rolling a die once. What is the probability of $2$ people getting the same number?

I am doing as following- $1^{st}$ people get a number from any $6$ number in $6$ ways, $2^{nd}$ people get a different number from rest of $5$ in $5$ ways, $3^{rd}$ people get another different ...
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### o(h) term in birth-death process

This is from the note I have two questions. Since $o(h)$ represents the probability of 2 birth and 1 death, 3 birth and 2 death, etc, why it still says $P(|X(t+h)-X(t)|>1)=o(h)$? shouldn't it ...
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