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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1answer
14 views

find the probability that, in the next 7 weeks, there are exactly 3 weeks in which Jan receives exactly 2 free gifts

Can you give me a breakdown of the stages you take arriving at the answer to the following question: Jan buys $5$ packets per week with a $30\%$ chance of finding a gift per packet,find the ...
0
votes
1answer
28 views

Poisson Distribution Greater than problem

A company manufactures long continuous lengths of computer network cable. The manufacturing process is not perfect, and sometimes faults are present in the cables. Faults occur along the cables ...
1
vote
1answer
22 views

Expected Value to grab a ball

Say we have $b$ blue balls and $r$ red balls in a urn. Randomly we grab a ball out of the urn, until we grab a blue ball. Now I want to find the expected value of the number of balls that have been ...
5
votes
1answer
60 views

Convergence of a sum of random variables

Let $(X_n)$ be a sum of i.i.d. positive random variables such that $\mathbb{E}(X_1)=1$ and $\mathbb{P}(X_1\neq 1)>0$. Put $M_n=X_1\ldots X_n$. Show that $\sum _{n\geq 1}\sqrt{M_n}< +\infty $ ...
-1
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0answers
17 views

Kino 90 numbers. You choose 10 numbers. What is the % of getting your number [on hold]

Kino 90 numbers. You choose 10 numbers. Starting from 1... to 90. There is a (say) 1/3 chance of this number being drawn. Example. Number 1... roll a 3-sided dice. I roll a 3--the number is drawn. ...
0
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0answers
19 views

Mean and standard derivation

A set of numbers consists of one's and three's. Find the mean and standard derivation if there are 23 one's and 17 three's. What's the meaning of this question ? I know the formula for mean and s.d. ...
0
votes
1answer
20 views

Finding the mode of the negative binomial distribution

The negative binomial distribution is as follows: $f_X(k)=\binom{n-1}{k-1}p^k(1-p)^{n-k}.$ To find its mode, we want to find the $k$ with the highest probability. So we want to find $P(X=k-1)\leq ...
2
votes
1answer
23 views

Using a markov chain to calculate the expected value of conditional/constrained choices (TopCoder PancakeStack)

I've been working on a programming challenge (link) where an expected value is calculated. Recently I learned about Markov chains and successfully applied them to solving a set of problems, but the ...
0
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1answer
16 views

Calculating Percentages/Probabilities of a Specific Scenario.

I've been trying for a few hours now to wrap my brain around, what at first, seemed like a simple concept. I've tried so many different things and ways of constructing scenarios so I can figure out ...
1
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2answers
29 views

Proving the $Pr(d>0|a+d=\pi)$ is increasing in $\pi$ when a and d are two independent normal distributions.

I was wondering if it is possible to prove the following (or show false otherwise). Given two independently distributed random variables $a\sim \mathcal{N}(\alpha,\sigma_\alpha^2)$ $d\sim ...
0
votes
2answers
19 views

Independent Events find P(A or B')

Given that P(A and B)=0.1 and P(A and B')=0.4 find P(A or B') if A and B are independent. The ans is 0.9 Please tell me the rule you use in the problem.
1
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1answer
27 views

Distance From Point to Nearest Value in Series

Let's say I have a point, chosen at random from the range [0, 1]. What is the average distance of this point to the nearest point in a set of n points chosen at random from the same range? ...
1
vote
1answer
29 views

Average number of tries needed before success

there is a 3% chance of success there are a thousand people trying over and over until they succeed how many tries will it take on average for the last person to achieve this success? I know that ...
1
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0answers
19 views

Compute the stationary distribution of a Markov Chain on an infinite state space

I have a Markov Chain on $\mathbb N_0^2$ with a given initial state $(x_0,y_0)$. The allowed transitions for example are of the following form: $(x,y) \mapsto (x-1,y+2)$ with probability $\propto x$ ...
2
votes
1answer
43 views

Mathematics of contamination [on hold]

I want to know the distribution of residual material (contamination) in subsequent refills. For example, suppose a cup normally used for transferring salt is used, without cleaning, for transferring ...
0
votes
0answers
6 views

How to get an approximation of $P(A\leq \max_{1\leq i\leq n}B_i)$,where $A, B_i$ are independent Gaussian random variables

Consider the independent Gaussian random variables, $A$, $B_1$,...,$B_n$. $B_i$ is distributed as $N(0,1)$. They are all independent. $A$ is distributed as $N(m,1)$. How can I approximate the ...
0
votes
1answer
31 views

It is true that $\int_{0}^{\infty}\mathbb{P}(x<m \ \cap Y \leq k-x) f_{X}(x)dx= \int_{0}^{m}\mathbb{P}( Y \leq k-x) f_{X}(x)dx$?

Let $X$ and $Y$ be independent random variables. Then it is true that? $$\int_{0}^{\infty}\mathbb{P}(x<m \ \cap Y \leq k-x) f_{X}(x)dx= \int_{0}^{m}\mathbb{P}( Y \leq k-x) f_{X}(x)dx$$ And, how ...
0
votes
0answers
20 views

Bayesian statistics and Basis for continous functions

I was thinking about Bayesian statistics, and one thought bothered me: In Bayesian statistics, we assume that the pdf $p(x)$ can be described as: $p(x)=\int f(x|\theta)g(\theta)d\theta$ usually ...
0
votes
2answers
31 views

Finding the mode of a distribution

I've been trying to get a better understanding of distributions. So far I understand how we get the formulas for mean and variance (by looking at the derivative of the moment generating function). ...
-1
votes
1answer
33 views

Help needed with Probability Question [on hold]

A card is drawn at random from a deck of playing cards. If it is red, the player wins 1 dollar; if it is black, the player loses 2 dollars. Find the expected value of the game. I think that the ...
4
votes
3answers
695 views

Probability of drawing a pair of brown socks

You have a drawer with $6$ loose blue socks, and $10$ loose brown socks. If you grab two socks from the drawer in the dark (random draw), what is the probability that you draw a brown pair? I have ...
0
votes
1answer
38 views

Rolling 1 die 5 times [on hold]

One die is rolled five times. How many different results are possible? Of those, in how many ways can there be exactly 2 rolls of 4?
2
votes
1answer
16 views

Conditional probability with max(X, Y)

Let $Y_n=$ the outcome of the $n$-th die roll, let $X_{n+1} = \max \{X_n, Y_{n+1}\}$ with $X_1=Y_1$. What is $P(X_{n+1}=j \ | X_1=i_1, ..., X_n=i)$? I know that it is $P(\max \{X_n, Y_{n+1} \}=j \ | ...
0
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0answers
16 views

multivariate interval estimation

I have several samples of probabilistic vectors, i.e, each sample is of the form $(x_1, \cdots, x_n)$ such that $\sum_{i=1}^n x_i\leq 1$ (they are sub-probabilistic vectors), how can I obtain a ...
-1
votes
1answer
30 views

probability for beginners : simple question [on hold]

Could you answer the following please... If we roll a die once and define Event A: The face value is even but less than 6 Event B: The face value is not 1 or 6. a) Then what is the ...
-1
votes
2answers
24 views

What is the probability of winning in a shootout? [on hold]

Person A can make $\frac{2}{5}$ of his free throws Person B can make $\frac{3}{4}$ of his free throws They take turns with person A going first The first person to make his free throw is the winner ...
0
votes
1answer
38 views

Understanding the sum of random variables

I am currently learning probability theory. I have two questions: I would like to know through an example what is meant by the sum of random variables (r.v.). To make things simple let consider only ...
1
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1answer
28 views

Proving a statement about probability theory

Let X be arandom variable. Consider any constant $c\gt 0$ how to prove the following satement $$\sum P(|X|\ge cn) \lt \infty \iff E(|X|)\lt \infty $$ My answer trail: $E[|X|]=\sum_X|X|P_x(X)\lt ...
1
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0answers
16 views

Suggestions for dealing with these order statistics

Consider a collection of $n$ random variables $X_i \sim N(\mu, \sigma^2)$, ($i = 1,2,\ldots, n$) and a random variable $X \sim \text{Exp}(\lambda)$. All $X_i$'s and $X$ are mutually independent. Let ...
1
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1answer
26 views

Bayes theorem - is it applicable in any case?

I'm studying the Bayes' Theorem and I have a doubt. In this wikipedia page there's an example of application for the following events: ...
0
votes
1answer
20 views

Calculating the probability of getting a full bucket in a hash table with open addressing

I have a problem where I'm trying to calculate the probability of getting a full bucket when I use a hash table with open addressing. What I have: A hash table with 128 buckets, each bucket can ...
1
vote
1answer
41 views

some properties of $\nu$ measure

For any given function $F$ satisfying the following properties $0\le F(x)\le1,\forall x\in\mathbb R$ $F(x)\le F(y),x\le y$ $\lim_{x\to-\infty}F(x)=0,\lim_{x\to\infty}F(x)=1$ $F$ is continuous from ...
0
votes
1answer
28 views

Simultaneous density function of two continuous variables, X and Y.

I'm having issues with calculating the simultaneous density function of two continuous variables, X and Y. I took a screenshot of the information: How should I start? I know that if the two ...
2
votes
1answer
15 views

How to find data distribution law using MATLAB?

Having a random variable $T \geq 0$ and a set of discrete data represented by $t=t_i$ and $P(T \leq t-i)$. My aim is to find the distribution law of $T$. Is there any fast method in Matlab that can ...
2
votes
0answers
24 views

Find the correct combination

Case 1 : if we bet on team1 with Rs.1 and win then we will get Rs.1+Rs.1 Case 2: if we bet on team2 with Rs.1 and win then we will get Rs.1+Rs.3 Case 3:if we bet on team3 with Rs.1 and win then we ...
2
votes
0answers
27 views

Hoeffding’s inequality extension

In Hoeffding’s inequality we assume that the random variables $X_i$ ,$i=1,..,n$ are i.i.d. and bounded . Is there any extension to Hoeffding’s inequality for the case that $X_i$ are identically ...
2
votes
1answer
22 views

Derive probability mass function from probability-generating function

Given the probability generating function $$G(z) = \frac{1}{2} \frac{3+z}{3-z}$$, how can one derive the pmf? I know that I have the manipulate the function into a series: $$G(z) = ...
1
vote
1answer
34 views

Understanding summations with Poisson

I'm currently doing a problem on Poisson processes and I've encountered the situation where I'm not sure why this summation is expanded as follows: And similarly I have tried expanding out the ...
1
vote
1answer
38 views

calculate a probability using the central limit theorem

$X$ is a variable of a Bernoulli distribution $ X \sim b(p)$ where $p\in(0,1)$. We also have the sequence of independent and identically distributed variables $Y_n$ with uniform distribution. $ ...
1
vote
1answer
31 views

Steve Nash’s expected value from his one-and-one free throw situation is 1.72 points. What is his free-throw percentage?

The one-on-one free throw situation works like this - for the first throw, if you make it, you get to do it again. If you miss, you don't get another chance. If you make it the second time, you get ...
1
vote
2answers
36 views

Why $p\{N>n\}=p\{X_1+…+X_n\leq x\}$.

Let $(X_k)$ a sequence iid of random variable uniform on $[0,1]$. Let $x\in]0,1[$ and $N=\min\{n\geq 1\mid X_1+...+X_n>x\}$. Why $$p\{N>n\}=p\{X_1+...+X_n\leq x\} \ \ ?$$
0
votes
2answers
54 views

Let X have density 2t on 0 < t < 1 and Y be uniform on the interval (0, 10) and independent of X. Find the density of Y/X. [on hold]

Let X have density 2t on 0 < t < 1 and Y be uniform on the interval (0, 10) and independent of X. Find the density of Y/X. Find E(Y/X) I have no ideas how to solve it now i ...
2
votes
1answer
48 views

Coin tossing: Streak count

I have a special request with regards to probability. Let's say I toss a coin 400 times. What I need to know is the average number of streaks of various lengths within such a sample. How many ...
1
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0answers
13 views

bias reduction when the bias depends on the true parameter

Let's say we estimate a parameter, $\theta$, by $\hat{\theta}$. For this estimator we have the following property that $$\hat{\theta}\to_{p}\theta+f(\theta)$$ where $\to_{p}$ denotes convergence in ...
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1answer
31 views

probability question of balls [on hold]

what is the chance of getting at least one defective item if 3 items are drawn randomly from a lot containing 6 items of which 2 are defective?
2
votes
0answers
25 views

normal squared characteristic function derivation

I'm trying to derive the normal squared characteristic function, there's already a question on this but the answer has a part which is "proved as an excercise" which I try to do here. Is my proof ...
4
votes
3answers
258 views

What is the probability that 5 randomly chosen cards in a deck add up to 40 or greater?

I have made a probability game, where you have to pull out any 5 cards without looking (from a deck of 52 cards), and if all five cards add up to 40 or more, they player pulling the 5 cards from the ...
0
votes
0answers
36 views

Sum of two independent Continuous-Time Markov Chains [on hold]

This is the first time I have come across a question involving the sum of two independent continuous time Markov Chains.I know you can find the sum of two random variables Z = X + Y by finding the ...
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votes
0answers
26 views

If the sequence of random variables $X_n$ converge in Probability to $X$ and $Y$, then $X = Y$ a.s. [on hold]

If the sequence of random variables $X_n$ converge in Probability to $X$ and $Y$, then $X = Y$ a.s. Idea: I want that $P(|X-Y|> \epsilon) = 0$, for every $\epsilon >0$. $P(|X-Y|> ...
6
votes
2answers
131 views

Rolling two dice, what is the probability that two consecutive $7$s happens earlier than a $12$?

Alice and Bob are playing a game involving two dice. If a sum of 12 appears, Alice wins and they stop playing. If a 7 appears twice in a row, Bob wins and they stop playing. What is the probability ...