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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3
votes
0answers
20 views

What is the area covered by a Random walk in a 2D grid?

I am a biologist and applying for a job, for which I need to solve this question. It is an open book test, where the internet and any other resources are fair game. Here's the question - I'm stuck on ...
1
vote
1answer
24 views

Probability of getting a five digit number divisible by 5 but with no two consecutive digits identical

A five digit number is written down at random. What is the probability of getting a number that is both divisible by 5 and doesn't have any 2 consecutive digits identical? I tried to analyse the ...
0
votes
1answer
28 views

An urn full of balls problem [on hold]

Among $10$ balls in a bag , $6$ of which are black , $4$ white , $3$ balls were removed randomly . What is the probability that from the remaining $7$ balls , if one ball is chosen at random , it is ...
-2
votes
1answer
23 views

a pin is spun on a flat table [on hold]

A pin whose centre is fixed on a flat table is randomly and independently spun twice.Each time the final position is noted by drawing a line segment.what is the probability that the smallest angle ...
1
vote
1answer
25 views

If 3 people put their hat in a box, but the hats are mixed up. How likely is it that AT LEAST one person getting their hat back.

If 3 people put their hat in a box, but the hats are mixed up. How likely is it that AT LEAST one person gets their hat back. Consider all possibilities. Then what about 4 people. Please use ...
0
votes
3answers
21 views

Probability rolling two different sided die and sum being a number

I'm building an app (for those curious, for DnD) and I came across an issue with some math I did. I need to know the probability of rolling a certain number when there are two or more different sided ...
-1
votes
0answers
29 views

boxes around a circle [on hold]

Suppose You have $10$ boxes numbered from $1,2,3,......,10$ arranged sequentially around a circle. We perform $100$ trials.At each step you have to choose a specific box with probability $\frac ...
-1
votes
1answer
51 views

How and why do rumors/gossip spread? [on hold]

I should clarify what I mean by gossip (this is taken from wiki): Idle talk or rumor, especially about the personal or private affairs of others. That seems accurate enough, though alternative ...
0
votes
0answers
12 views

Regression in Bivariate Normal

Suppose $(X_i \hspace{4pt} Y_i)'$ are $i.i.d$ $N_2 (\bf{\mu,\Sigma})$, $i=1(1)n$ where $E(X)=\mu_x$, $E(Y)=\mu_y$ and $\Sigma$ is given by \begin{bmatrix} \sigma^2_x & \rho\sigma_x\sigma_y\\ ...
0
votes
0answers
14 views

Find conditional probability of a mixture model

given is the following: A mixture model comprises a non-observable $\{ 0,1\}$-valued random variable $X$ such that $P(X=1)=1-P(X=0)=\pi$ and an observable variable $Y$ such that $Y\mid X=0$ is ...
1
vote
1answer
20 views

Probability a card can win a trick with a trump suit

I'm working on the AI for a card game that uses a standard deck of 52 cards consisting of 13 cards in 4 (spades, clubs, diamonds, hearts) suits. Each player starts with 13 cards in their hand. ...
3
votes
4answers
122 views

What is the probability of getting a 3 or higher on a six sided die, if I reroll after failing the first time?

Just as the question says... What is the probability of rolling a 3 or higher on a six sided die, if I reroll the die a second time when I fail the first time?
0
votes
0answers
50 views

Question about conditional probability [on hold]

I am working on some exercise questions from probability. I am stuck at this question. Can somebody help me to solve this. I would really appreciate. In a certain country, $35$ percent of people ...
0
votes
0answers
13 views

Picking Marbles and Estimating the Expected Cost

This is a general version of a game I play. Suppose there is a bag of marbles that consists of 4 different marbles : Silver ...
0
votes
0answers
27 views

Probability of Level Crossing

I am kind of stuck on how to proceed on this. $X_n$ is an IID process with $$f_{X_n}(y)= \frac\lambda2 e^{-\lambda |y|}$$ There is a stationary autoregressive process $Y_n$ defined as $$Y_n=\rho ...
0
votes
0answers
35 views

what is the difference between statiscal averagre and average?

I'm reading a book on synthetic aperture radar and it is said that: The term $\sigma^{\circ}$ is the averaged radar cross section per unit area, also called the scattering coefficient or ...
1
vote
2answers
57 views

Ways of coloring the $7\times1$ grid (with three colors)

Hints only please! A $7 \times 1$ board is completely covered by $m \times 1$ tiles without overlap; each tile may cover any number of consecutive squares, and each tile lies completely on the ...
0
votes
1answer
33 views

Prove that if events $A,B$ independent of C then $P(A\cap B\cap C)= P(A\cap B)P(C)$

I am trying to prove why the intersection of two events $A, B$ that are independent of C is also independent of C so that the following equality holds: $$P(A\cap B\cap C)= P(A\cap B)P(C)$$ ...
0
votes
1answer
12 views

What am I plugging in wrong to my normal distribution calculator?

I am trying to find the probability of the following question: Cans of regular Coke are labeled as containing 12 oz. Statistics students weighed the contents of 7 randomly chosen cans, and found the ...
1
vote
1answer
15 views

Discrete-time Markov Chains

I am having trouble understanding this proof from Markov Chains by Norris (1997) How do we get the equality $P_j(X_n=j \text{ for infinitely many } n ) =P_j(X_n=j \text { for some } n \ge m+1)$ ?
1
vote
1answer
29 views

Is there any difference between statistical learning and machine learning?

Straight to the point, I'm a math student and I have a course this year called Statistical Learning. From the description, the course contains: Large datasets analysis, regression, principal ...
1
vote
1answer
15 views

Expected Shortfall alternative definition

Define: $$q_\alpha(F_L)=F^{\leftarrow}(\alpha)=\inf\lbrace{x\in \mathbb{R}\mid F_L(x)\geq \alpha\rbrace}=VaR_\alpha(L)$$ I want to prove that: $$ES_\alpha = ...
1
vote
1answer
26 views

Distribution Technique Question of two independent Exponential Distributions

If $X_1$ and $X_2$ are two independent random variables having exponential densities then $f(x_1,x_2)$ is defined as $$f(x_1,x_2)=\exp(-(x_1+x_2))\,{\bf 1}_{(0,\infty)}(x_1){\bf ...
-3
votes
0answers
29 views

Regression in Statistics [on hold]

A survey was carried out by a lecturer on a small random sample of her students, in which she asked them individually how much time, $y$, they spent studying and how much time, $x$, they watched ...
-1
votes
0answers
23 views

the joint probability density

The joint probability density f(x, y) of a pair of random variables X and Y is zero everywhere except on and inside the L- shaped region shown in the following plot, in which the density is some ...
-1
votes
1answer
32 views

Probability, step function [on hold]

A one-dimensional random walk starts at the origin x = 0 at time t = 0, and takes a random step of either +1 or -1, every second. It takes a total of 4 random steps altogether, with the final location ...
0
votes
0answers
22 views

Weighting the data by the history

I have a input stream 3D data that comes every time frame. Each point is defined by 3D vector of x,y,z. There is a evaluation function [say f(x)] that computes if the point at time t is valid or ...
2
votes
1answer
37 views

How many 3 letter words can you form from 'EEAAP' [duplicate]

How many 3 letter words can you form from 'EEAAP' I think the answer is ${3\choose 3} * 3! + {2\choose 1} * 3 + {2\choose 1} *3=18$. Is this right? ${3\choose 3} * 3!$ = You pick all ...
1
vote
2answers
44 views

Runs of white balls in sampling without replacement

There are $m$ white balls and $n$ black balls in a box. Balls are randomly drawn from the box with no return. Denote $X_1$ : number of white balls that been drawn before the first black. For $2 \leq i ...
3
votes
1answer
46 views

How many ways can you choose team of 5 people out of 7 men and 6 women in which there are at least 3 men?

I am confused by this question. I solved it by selecting 3 men first out of 7 men and then selecting 2 people out of 10 remaining person ( 4 men and 6 women ) . So my answer is C(7,3) * C(10,2) = ...
3
votes
1answer
31 views

Probability of the card following first ace being ace of spades or two of clubs

I am learning probability from Scheldon Ross' book. The question reads like this: A deck of 52 playing cards is shuffled, and the cards are turned up one at a time until the first ace appears. Is ...
1
vote
1answer
36 views

How do I go about solving this probability question?

I was playing around with dice this morning and flipping them, when a problem suddenly hit me. If I roll $n$ normal six-sided dice, and flip every single dice, what is the probability that the ...
0
votes
2answers
36 views

Probability and Combinatorics

I am trying to solve example 4.15 here but think the total number of outcomes in the solution is incorrect. This is my reasoning. We have 3 that qualify as best three, say BBB, and 2 as bad say OO. ...
1
vote
0answers
16 views

Quantum probability and quantum measure theory

Do quantum probability and free probability mean the same thing - that is, they deal with noncommutative random variables? What about quantum measure theory? Is quantum measure theory the foundation ...
1
vote
1answer
23 views

determination of probability

Recently I have faced a problem related to probability.I have tried it by bayseian theorem but failed.Here is the problem: A doctor knows that pneumonia causes a fever 95% of the time. She knows that ...
0
votes
0answers
23 views

A Feynman-Kac style derivation of a survival probability of a Compound Poisson process

Let $$R_t = u + \beta t - \sum^{N_t}_{i=1}U_i$$where $u\geq 0$, $\beta > 0$, $N_t$ is a Poisson counting process with intensity $\lambda$ and $U_i$ are jumps having a probability density $\nu(y)$ ...
2
votes
2answers
33 views

What is the variance of the volumes of particles?

According to Zimmels (1983), the sizes of particles used in sedimentation experiments often have a uniform distribution. In sedimentation involving mixtures of particles of various sizes, the larger ...
0
votes
2answers
30 views

Class Coin Toss Experiment

My classmates and I are doing a coin toss experiment (i.e. toss coin 100 times). I have already determined that I have a fair coin, since I tossed $43$ heads, and this falls into a $95$% confidence ...
0
votes
1answer
30 views

Expected value and single event probability [on hold]

Can expected values be added together to represent the overall expected value of a single event? Or is there a different way to do expected value for a group of probabilities? Also if I have 10 bets ...
-2
votes
0answers
21 views

What is the proof behind the mean confidence interval for a Binomial Distribution?

How do we obtain the range to be as [$\mu-$$zσ$, $\mu+$$zσ$]? Is it when $n$ is sufficiently big?
2
votes
0answers
32 views

Probability of a run of *k* or more of a subset of categories in *m* multinoulli trials?

Given a multinoulli distribution of categories $(C_1,C_2,...,C_n)$ with associated probabilities $\left\{p_1,p_2,\ldots ,p_n\right\}$ with $\sum _{i=1}^n p_i=1$, is there a tractable way to get the ...
-1
votes
0answers
31 views

Odds for rolling specific faces on a 3-sided die [on hold]

Firstly, thank you for taking my question! Imagine five (5) $3$-sided dice, so three unique faces. What are the odds (percentage) of rolling $3$ of the same face when rolling $5$ dice? When rolling ...
-5
votes
1answer
27 views

lottery question [on hold]

for the lottery -- if I have 4 numbers How can I see all of the 4 number combinations, never using the same number more than once in each combination. the numbers used will always only be a ...
-3
votes
2answers
49 views

100-sided dice was rolled 98 times, how do you choose next numbes to bet, based on current outcomes.

100-sided dice was rolled 98 times, Numbers form 1 to 50 were rolled exactly once, except number 25, which wasn't rolled yet. Number 75 was rolled 49 times You can only bet if the next roll result ...
2
votes
3answers
278 views

Is the limit of càdlàg functions càdlàg?

Is the pointwise limit of càdlàg functions càdlàg? If not which are the weaker conditions to assure it? I cannot find a counterexample
0
votes
1answer
21 views

Is there an upper bound for expectation of product of two measurable function on a random variable?

I wonder if there is an useful upper bound for $\mathbb{E}_{x\sim p(x)}[f(x)g(x)]$ in the following form: $$ \mathbb{E}_{x\sim p(x)}[f(x)g(x)] \leq \mathbb{E}_{x\sim p(x)}[f(x)]\times xxxxxx $$ The ...
-2
votes
0answers
48 views

Probability - There is a radar, a computer and a gyroscope [on hold]

There is a radar, a computer and a gyroscope on board an airplane. The probability that the radar fails is 0.2. If the radar fails, the gyroscope will also fail, and the probability that the computer ...
4
votes
2answers
88 views

Combinatoric Birthday Paradox

There is likely a closed form solution for this problem but it's had me puzzled for days. This is about a variant on the classic birthday paradox. To recap, the birthday paradox is where given only 23 ...
-1
votes
1answer
15 views

Distribution of specific distributions

I have a normal distribution of independent variables, and there are a specific number of samples to this distribution: say 1 million samples. A function is set by the largest value of these million ...
-2
votes
0answers
21 views

Scrabble/words with friends [on hold]

How many letter combinations are possible with 7 tiles? Just the math answer please, 7 tiles in 7 slots, how many different combinations? Thank you :)