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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2answers
17 views

Find the fraction where the decimal expansion is infinite?

Find the fraction with integers for the numerator and denominator, where the decimal expansion is $0.11235.....$ The numerator and denominator must be less than $100$. Find the fraction. I ...
-1
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0answers
7 views

Random Walk With Absorbing Barrier

Consider a random walk $S_t$ with a lower absorbing barrier at $0$, and no upper absorbing barrier. $\mathbb P(S_{t+1}-S_t=2.5)=0.5$ and $\mathbb P(S_{t+1}-S_t=-1)=0.5$. What is the probability of ...
0
votes
1answer
16 views

$P(X=c)=0$ for normally distributed $X$?

Let $X$ be norm $(a, b)$-distributed and let $c$ be some real number. Does this imply $P(X=c)=0$? What if $b=0$?
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0answers
4 views

A treatise on Probabilistic arguments (or even Laplace/Fourier transforms) to solve limits/integrals from basic calculus.

I've seen in some answers in Brilliant.org to some very complicated limits and integrals that uses probabilistic arguments (Let $X$ be a random variable from $[0,1]$... some examples are in those ...
1
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0answers
13 views

Calculate expected values of the lengths of line segments

There is a line segment of the length of $1$. $N-1$ points are randomly chosen in it, so it is divided by $N$ parts. The question is to calculate expected values of all these parts, from the shortest ...
0
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1answer
10 views

definition of Cumulative distribution function

let X be RV, and his Cumulative distribution function: there is a difference if in my case if $X<x$ ? the definition is the same?
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2answers
42 views

Probabilistic arguments in calculus

As the book Probabilistic Techniques in Analysis by R. Bass shows, there is a huge interplay between analysis and probability. However, I would like to see some examples of "more basic" relationships ...
2
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0answers
22 views

Prove that $\int k(w)o(h^2w^2)dw=o(h^2)$ for $\int k(w)dw=1$

Suppose that $k$ is nonnegative real-valued function satisfying $$ \int k(w)dw=1,\quad\int wk(w)dw=0,\quad\int w^2k(w)dw=\kappa_2<\infty.\tag{$\star$} $$ Can you please teach me a rigorous ...
0
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3answers
43 views

Probability when n balls put randomly in n boxes such that each box contain 1 ball [on hold]

There are 100 boxes in front of you. You have 100 balls in your pocket which you throw one by one towards the boxes in front of you. Each ball will definitely end up in a box and has equal probability ...
2
votes
2answers
28 views

Probability in dice, Feller exercise

I am stuck with exercise 2 of Chapter 4 Feller vol 1 "an introduction to probability theory and its application". Here I report the exercise text: Five dice are thrown. Find the probability that at ...
-2
votes
0answers
17 views

Probability (Dependent Events) [on hold]

The M.com class consists of 60 students, 12 of them are girls and 48 boys, 10 of them are rich and 50 not, 15 of them are fair complexioned. What is the probability of selecting a fair complexioned ...
2
votes
1answer
18 views

Derivation of the third moment of Poisson distribution using Stein-Chen identity

(a) Use LOTUS to show that for $X \sim \operatorname{Pois}(\lambda)$ and any function g, $E(Xg(X)) = λE(g(X + 1))$. This is called the Stein-Chen identity for the Poisson. (b) Find the third ...
0
votes
3answers
34 views

Where does this conditional probability law come from?

I was trying to follow a computation done in my class notes, and was having difficulty seeing the inspiration for a part of the manipulation in a question regarding probability. I did some Googling, ...
1
vote
0answers
9 views

Deviation of number of cycles of length 4 in Erdős–Rényi random graphs.

I'm working on my homework and can't find any relevant information for this problem. Problem: Let $G(n, p)$ be Erdős–Rényi random graph. I need to find deviation of number of cycles of length 4 in ...
0
votes
1answer
22 views

Two series of independent Bernoulli trials. Find distributions of being simultaneously successful and of first success being simultaneous.

Nick and Penny are independently performing independent Bernoulli trials. For concreteness, assume that Nick is flipping a nickel with probability p1 of Heads and Penny is flipping a penny with ...
0
votes
0answers
29 views

Can somebody help to understand the last step of this proof?

PLEASE look this proof first. Suzu Hirose helped me a lot! But I still do not understand the last step:(Suzu explained the fist several steps to me in this page :Explanation of an integral formula ...
5
votes
2answers
38 views

Distributing candies

Suppose ther are B boys and G girls in a classroom.Teacher wants to distribute candies among B boys and G girls such that: 1.Each student gets atleast one candy and atmost N candies. 2.sum of ...
1
vote
2answers
28 views

problem related with probability [on hold]

Three shots are fired in succession. The probability of a hit in the first shot is 0.3, in the second is 0.6, in the third is 0.8. In the case of one hit, the probability of destroying the target is ...
0
votes
0answers
30 views

Who can find mistakes in this calculation process?

I compute the conditional Separman's rho using the following method, but I do not know whether it is right? Who can tell me whether it is right? Thanks.
1
vote
1answer
60 views

Explanation of an integral formula for the expectation of $(X_1-X_2)(Y_1-Y_2)$

I do not understand the proof of this expression. Who can explain it to me using simpler words? I do not understand the following black part:
3
votes
1answer
41 views

probability circle determined by chord determined by two random points is enclosed in bigger circle

Two points $A$ and $B$ are chosen uniformly at random from the interior of a circle $X_1$. Let $X_2$ be the circle whose diameter is the segment $AB$. What is the probability that $X_2$ is contained ...
1
vote
2answers
37 views

Health Risk Probability

Question: An actuary is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of women. For each of the three factors, the probability is 0.1 that a woman ...
2
votes
1answer
34 views

Chance of winning a game of hearts with four players

I play hearts with a computer game program. The game is set up so that four people are playing the game. The question is: What are the mistakes, if any, with assuming that the probability of winning a ...
0
votes
0answers
24 views

How to calculate the following conditonal expectation? am I right?

How to calculate the following conditonal expectation? Is the following calculation process right?
1
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0answers
21 views

How to calculate the following conditional expectation? Is my calculation process right?

I want to calculate the conditional person's correlation coefficient. But I don't know how to calculate the following expressions,especially the conditional expectation of ...
9
votes
2answers
78 views

true story about probability? [duplicate]

A women's organization was contemplating suing a famous American university when it learned that the percentage of women who received tenure in the university was smaller than the percentage of men. ...
3
votes
2answers
40 views

Choosing exactly 2 damaged pieces (Probability)

From $27$ pieces of luggage, an airline handler damages a random sample of $4$. The probability that exactly one of the damaged pieces of luggage is insured is twice the probability that none of ...
1
vote
1answer
36 views

What does it mean to say the smallest σ-algebra?

I am just starting out on measure theory. What does it mean to say the smallest σ-algebra?
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votes
4answers
118 views

How can I write this power series as a power series representation?

How can I write this power series ($1+x+2x^2+2x^3+3x^4+3x^5+4x^6+4x^7+5x^8....$) as a power series representation (like $\dfrac{1}{1-x}$ or something neat like that)?
-9
votes
0answers
37 views

Stochastic Process random process. [on hold]

I need answer PLEASE FULL DETAILS ABOUT STOCHASTIC PROCESS
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0answers
34 views

Stochastic Process random process [on hold]

Full Details please about the stochastic process ( random process)
1
vote
0answers
12 views

the quantile to quantile plot for the discrete law

the quantile to quantile plot works good for the continuous law. But I don't know why it doesn't work for the discrete law, example the law Poisson. Please help me
0
votes
1answer
24 views

Using Poisson distribution to find the probability that the interval between arrivals exceeds some value

Suppose we have a helpdesk with tickets arriving at a rate of three per min. Tickets arrival follow a Poisson distribution. How someone can calculate: a. The probability of the time between the first ...
2
votes
3answers
36 views

Probability of winning a rigged coin-flipping game

Betsy and Katie are playing a game with an unfair coin. The coin is rigged to come up heads with probability $\frac35$ and tails with probability $\frac25$. Betsy goes first. The two take turns. The ...
2
votes
5answers
75 views

Jamie rolls a die multiple times. find the probability that she rolls her first 5 before she rolls her second even number

Jamie rolls her fair 6-sided die multiple times. Find the probability that she rolls her first 5 before she rolls her second (not necessarily distinct) even number? This is what I have so far... ...
0
votes
4answers
55 views

Expectation of non-negative random variable

Let $X$ be a non-negative random variable. In a proof for $E[X]=\int_0^\infty P(X>t)dt$ from the answer of this question, we use Fubini for the middle quality. Why do we need $X$ to be ...
2
votes
4answers
66 views

How to find the number of possible outcomes of 10 games between 20 teams?

Hi I am looking for an equation to find possible combinations in a non repeating format with a twist. Here is the example: There are 10 games between 20 teams. I have to chose 5 winners but ...
1
vote
1answer
28 views

$G_n:=\sqrt{n} \left(X_n-1\right) \xrightarrow[n]{d} N(\mu,\sigma^2) $ implies $\sqrt{n} \left(1-X_n^{-1}\right)=G_n+o_P(1)$

Let $X_n$ be a sequence of RV so that $G_n:=\sqrt{n} \left(X_n-1\right) \underset{n \to \infty}{\overset{d}{\longrightarrow}} G \sim N(\mu,\sigma^2)$. I want to show that in this case $\sqrt{n} ...
2
votes
1answer
21 views

Finding the PDF from the CDF where the CDF is not differentiable at some point

I got the following problem: Let $X$ be a continuous random variable with $CDF$ denoted $F_X$ defined as follows: $F_X(x)= \begin{cases} 1-x^{-4/3}, & x\in[1,\infty) \\ 0, & x\in ...
0
votes
0answers
16 views

Find probability density function of random vector

Random vector has continuous distribution of setA={(u,v), v>=0, u+v<=1, v-u<=1}. I need to find joint probability density function of this vector. In my ...
0
votes
0answers
10 views

Limit distribution on return time $\tau = \inf\{k: X_k = X_m \text{ where }m<k\}$ [on hold]

Suppose there is a stochastic process ${X_i}_{i=1}^n$ where $X_i$ is distributed normally over $\{1,\dots,n\}$. As $n\rightarrow \infty$, the probability that any one value is repeated should go to ...
-4
votes
0answers
47 views

Where can I find consultants on Long Lead Coin Tossing Experiments? [on hold]

Where can I find consultants on Long Lead Coin Tossing Experiments? I am specifically interested in the phenomenon of Long Leads, which was discussed in Feller's classic text. I want somebody to ...
0
votes
0answers
6 views

What is the formula for the 2-sample Anderson–Darling upper tail test?

There are computationally simple formulas for the Anderson–Darling test between an analytic distribution and an empirical distribution, as well as for the Anderson–Darling upper tail test (again ...
0
votes
1answer
32 views

The number of self-avoiding paths in the plane of length $k$

The number of self-avoiding paths in the plane of length $k$ is at most $4 \cdot 3^{k-1}$ according to this. Why? My immediate thought: four options for the first move and always three choices after ...
0
votes
2answers
38 views

Ladybug walking on a hexagon probability question [on hold]

A ladybug is walking at random on a hexagon. The ladybug begins at Vertex A. Each minute, the ladybug moves to ONE OF the randomly chosen TWO vertices adjacent to the one she's currently on. Find ...
0
votes
3answers
54 views

How many ways to make a connected graph using 4, 5, 6 edges?

How can/how many ways can you make a connected graph that has 5 vertices using 4, 5, 6 edges? I'm not sure how it would look like for 4 edges. Can you draw a diagram?
1
vote
2answers
42 views

Interchanging the order of a double infinite sum

I'm stuck at a proof of Wald's first equation about interchanging the order of a double infinite sum: Suppose $X_n \ge 0$ and $1_{\{\cdot \}}$ be indicator function. $$ \sum_{n=1}^\infty ...
0
votes
2answers
41 views

central limit theorem, solving for probability

I am playing a game and am trying to calculate the probability that I will win at 40,000 or more points total, if I play the game 1,000,000 times. The expected value for one game is zero and the ...
1
vote
1answer
17 views

Probability: Expectation: indicator RV, what is 1-((N-1)/N))^n?

Say there are N coupon types, you collect n coupons, and what's the expected number of types of coupons? My question is specifically about $1-(\frac{N-1}{N})^n$, the probability of getting a coupon ...
-1
votes
1answer
80 views

$3$ dimensional light up cube ornament, # of rows/cols/diags in/on a cube

Imagine a $3$ dimensional cube (much like a $4\times4\,(\times4)$ Rubik's cube) except the planes of the cube cannot be twisted individually and instead of faces with different colors, it is clear ...