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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36 views

Generating structure of Borel field

On P.32 of [P.Billingsley] Probability and Measure, 3ed, 1993, the author wrote: ...and there are Borel sets that cannot be arrived at from the intervals by any finite sequence of set-theoretic ...
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4answers
817 views

What is the expected length of the largest run of heads if we make 1,000 flips?

Is there a way to calculate on average, the maximum amount of times we can expect a coin to land heads during 1,000 flips? So the answer (and formula if one exists) I am looking for would be ...
2
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0answers
23 views

Example of a bounded simple process $A_t$ that changes value only once s.t. $\int_0^t A_s dB_s$ doesn't have normal distribution?

As the title of the question suggests, what is an example of a bounded simple process $A_t$ that changes value only once such that$$\int_0^t A_s\,dB_s$$does not have a normal distribution?
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1answer
45 views

A coin probability question

Let $p$, $q$ be values in $[0,1]$ and $\alpha \in [0,1]$. Assume $\alpha$ and $q$ known, and that $p$ is unknown parameter we would like to estimate. A coin is tossed n times, resulting in the ...
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2answers
17 views

Probability Distributions (Tree Diagram)

Satish picks a card at random from an ordinary pack. If the card is ace, he stops; if not, he continues to pick cards at random, without replacement, until either an ace is picked, or four cards have ...
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0answers
11 views

the meaning of 4-wise hash function

If someone says: 4-wise independent sign (hash) functions $s_1,s_2, s_3 : [d] → \{+1, −1\}$, then what does it means? I cannot use k-wise Independence variables (the definition 1 ...
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0answers
12 views

Hypothesis Testing with given Pearson correlation.

There are two independent sets of samples , female and male. The problem is to calculate the 95 % C.I. of the mean of total( male+ female, two samples) population. -> Female : n=100, mean= 169.1, sd ...
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1answer
22 views

Combining probability percentages or fractions

If I have a bag with 4 different color marbles, one of the colors being green, then I am assuming that the chance of drawing the green marble on the first attempt would be 1/4 or 25% or 3 to 1 ...
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2answers
25 views

Using Normal Distributions to find Proportion

The height of a randomly selected woman from a population is normal with $\mu=165cm$ and $\sigma=7cm$. The heights f the men in this population are normal with $\mu=178cm$ and $\sigma = 8cm$. I am ...
2
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3answers
104 views

Probability that the eventually a six on a dice will appear.

Dave rolls a fair six-sided die until a six appears for the first time. Independently, Linda rolls a fair six-sided die until a six appears for the first time. Let $ m$ and $ n$ be relatively prime ...
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2answers
23 views

Generating points from 2 Normal distributions and $0$-probability continuous r.v.s

Consider the following experiment: We generate "green" points and "blue" points in $\mathbf{R}$ using two different normal distributions as follows: 1000 green points are sampled from a $N(-1, 1)$ ...
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0answers
21 views

In a special deck of playing card, one which doesnt contain any Jack, Queen or King [on hold]

Determine the probability of the following events: a. Drawing a space (one card) b. Drawing a black card (one card) c. Drawing of four hearts ( four card) d. Drawing of full house (five cards) e. ...
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1answer
34 views

Measurability of marginal distributions of a random measurable function

For a probability space $(\Omega, \mathcal F, \mathsf P)$, let $X \colon \Omega \times [0,1] \to \mathbf R \colon (\omega, t) \mapsto X(\omega,t)$ be a random Borel function (i.e. an $(\mathcal ...
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0answers
24 views

PROBABILITY- (A1,A2…F30)

I have one rectangular board. It has row A,B,C,D,E,F AND columns 1,2,3,4,5 UPTO 30.So totally 180 boxes are there. Each boxes in the name A1,A2....like that each boxes has separate names. Could you ...
2
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4answers
137 views

Summing n times binomial(n,k)

I'm trying to do $\sum_{n=a}^b \left( \begin{array}{rl} n \\ a \end{array} \right) n $ . Is there a formula, that anybody knows?
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0answers
19 views

probabilty involving 3 components [on hold]

There are 6 blue balls and 10 red balls. What is the probability of 9 persons getting blue balls? Please help me. Thanks.
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0answers
126 views

The mathematics of a drinking game called Spoon

This question is about the drinking game Spoon. It was asked on reddit.com/r/math : http://www.reddit.com/r/math/comments/3i9790/drinking_game_turned_mathematical/ The question is whether the person ...
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1answer
32 views

Probability of 2 integers selected are the same is greater than 0.7 in random generated set of 14 intergers. [on hold]

A set of 14 random generated integers between (inclusive) 10-30 are generated (repetition is allowed, meaning that it is possible of 2,3 or more random generated integers are same), how many number of ...
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3answers
33 views

Finding the Marginal Distribution of Two Continuous Random Variables

The continuous random variables $X$ and $Y$ have the joint probability density function: $$f(x, y)= \begin{cases} \dfrac{3}{2}y^2, & \text{ where } 0\leq x \leq 2 \text{ and } 0 \leq y ...
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1answer
11 views

Do the bounds change when multiplying a probability distribution by a constant?

Do the bounds change when multiplying a probability distribution by a constant? For example consider when an exponential distribution bounded by upper bound A, lower bound B and mean X, is multiplied ...
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7answers
507 views

What is the probability that Sam has drawn a card greater than Ram.

Ram draws a card randomly among cards numbered 1-23 and keeps it back. Then Sam draws a card among those left. What is the probability that Sam has drawn a card greater than Ram? My Approach: I ...
0
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1answer
56 views
+50

What is the probability that no two consecutive boxes have blue balls.?

There are red and blue balls which can be filled in 5 boxes.All balls are similar except color. what is the probability that no two consecutive boxes have blue balls. Assume:A ball can be either ...
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2answers
21 views

What is the Probability that the remaining marble from the same bag is also white given 3 bags each containing 2 marbles.?

You have 3 bags each containing two marbles. Bag A contains 2 white marbles , Bag B contains 2 black marbles, Bag C contains one white marble and one black marble. You pick a ...
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5answers
65 views

Finding amounts of ingredients in a food based on nutrients

Imagine that there are 50 ingredients, $I_{(1-50)}$, cake can possibly be made out of. Our friend makes a cake from unknown amounts of these ingredients. Therefore the cake $C$ is composed as such: ...
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2answers
18 views

Ram shoots every third penalty to goal.If he gets chance to shoot all 5 penalty shots.What is the probability that he converts (does) exactly 3 goals.

Ram shoots every third penalty to goal.If he gets chance to shoot all 5 penalty shots.What is the probability that he converts (does) exactly 3 goals. My Approach: p(Ram for every 3rd goal)=1/3 ...
0
votes
1answer
22 views

Univariate Normal Distribution Transformation

X is the time taken for a high school athlete to complete a 100m sprint, in seconds, which follows a normal distribution with a mean of 16. The athlete would complete the sprint under 19.495 seconds ...
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0answers
18 views

pick a sequence of parameters to preserve original convergence

Suppose for any fixed $\delta >0$, we have $$X_n(\delta) \overset{\mathbb{P}}\to 0 \quad \text{as}\ \ n \to \infty.$$ Does there exist a sequence $\delta_n \to 0$ such that $$X_n(\delta_n) ...
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2answers
27 views

Modulo question: $(\operatorname{rand}[0,n-1]+\operatorname{rand}[0,n-1]+\cdots+) \pmod n$?

I have a problem: There are $i$ betters, each choose a random value between [$0$ and $n-1$] Then we add all the $i$ numbers and we do (mod $n$) $$\text{Final number}= ...
1
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1answer
25 views

Covariance of Ornstein-Uhlenbeck process

$U(t)=e^{-\mu t}W(\frac{\sigma^2e^{2\mu t}}{2\mu})$. The problem is to find $Cov[U(t),U(t+s)]$. I used the identity, $W(\frac{\sigma^2e^{2\mu t}}{2\mu})=W(\frac{\sigma^2e^{2\mu t}e^{2\mu s}}{2\mu ...
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1answer
56 views

Breaking probability theory by having a different number of random variables depending on a conditioning random variable.

I suspect I'm breaking probability theory but I don't know how or why. How does one handle working with conditional probabilities where one can have a different number of random variables depending on ...
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2answers
27 views

What is the probability of drawing at least one of each of these cards?

Say you have a deck of cards that contains $n$ total cards. $x$ amount of these are Card A $y$ amount of these are Card B $z$ amount of these are Card C By drawing $m$ cards at random from this ...
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0answers
40 views

Sufficient condition for convergence in distribution in the plane

I'm trying to show convergence in distribution for a sequence $X_n$ of random variables in the plane. Here's what I know. I have a sort of squeeze theorem for the probability of the r.v.s being in a ...
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0answers
26 views

Minimizing 2-norm of a random vector by translation

Let $X$ be a random vector in $\mathbb{R}^n.$ The quantity $\mathbb{E}||X-a||_2^2$ is minimized by the choice $a_i=\mathbb{E}X_i$ for all $i.$ The quantity $\mathbb{E}||X-a||_1$ is minimized by the ...
2
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1answer
45 views

Expected norm of a random Gaussian vector

Let $X$ be a random vector in $\mathbb{R}^n$ whose entries are joint Gaussian with zero mean and covariance matrix $K.$ Is there a closed form expression for $\mathbb{E}||X||_2,$ as there is for the ...
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1answer
44 views

Given a $4\times 4$ Matrix having $16$ points, what is the probability of making a triangle?

Given a $4\times 4$ Matrix having $16$ points, what is the probability of making a triangle from these points? My Approach: $4\times 4$ matrix has $16$ points. So, I can choose 3 point of a ...
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1answer
23 views

How to find a conditional probability density function

How to find the conditional probability density function $P(X>Y\mid \max(X,Y)>T)$. $X,Y$ are independent identical exponential random variables. $T$ is a constant. Is it possible to find at ...
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1answer
42 views

Probability that 4 friends will be in the same class

A group of 60 second graders is to be randomly assigned to two classes of 30 each. Five of the second graders, Marcelle, Sarah, Michelle, Katy, and Camerin, are close friends. (a) What is the ...
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3answers
62 views

Probability of getting 4 aces in a stack of 52 cards

A deck of 52 cards is shuffled thoroughly. What is the probability that the four aces are all next to each other? What i tried To choose the first ace i took $ \left( \begin{array}{c} 13 \\ ...
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5answers
46 views

Probability of getting heads in a coin toss

A fair coin is tossed five times. What is the probability of getting a sequence of three heads? What i tried Since the probability of getting a head and not getting a head is $0.5$. The probability ...
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1answer
74 views

Hitting a line in a $d$ dimensional cube

Let $F$ be a finite field of order $n$, and let $d$ be an integer. A line in $F^d$ is a function $\ell: F \to F^d$ given by $\ell(t) = x + t*h$, where $x,h \in F^d$, $h \neq 0$, and $t*h = (tx_1, ...
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1answer
70 views

Does this game make you arbitrarily rich with probability one?

We toss a coin. If it's heads we win $\$ 1$, otherwise we lose $ \$ 1$. Fix some large sum. Will we be winning this amount with probability one at some point? We assume that we have infinitely many ...
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1answer
39 views

Does it mean “two successive tosses is the same” is same as “two successive tosses is either heads or tells”?

I got confusion ! Does it mean "two successive tosses is the same" is same as "two successive tosses is either heads or tells" ? I have two problems : Q. I have an unbiased coin , assuming ...
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1answer
29 views

Find the maximum value of the quotient

Given a real number $x,$ let $\lfloor x \rfloor$ denote the greatest integer less than or equal to $x.$ For a certain integer $k,$ there are exactly $70$ positive integers $n_{1}, n_{2}, \ldots, ...
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4answers
89 views

Binomial Distribution - probability of winning 3 or more lottery prizes if you buy 1 ticket per week

The question asks: Suppose that in a weekly lottery you have probability .02 of winning a prize with a single ticket. If you buy 1 ticket per week for 52 weeks, what is the probability that you ...
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2answers
32 views

Probability of getting a exact sum of 20 given a person has 5 coins in his pocket and the coins are of only 3 denominations 1,2 and 5.

A person has 5 coins in his pocket. In India coins are of only 3 denominations 1,2 and 5. He takes out coins in his pocket.What is the probability of getting an exact sum of 20? My Approach in ...
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1answer
55 views

Probability that the tenth card is black if at most one was black out of the first nine

Assume you draw 10 cards from a standard 52 card deck without replacement. What is is the probability the 10th card is black for the two cases below: a) the first nine cards drawn are not ...
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1answer
46 views

What does “this probability density function is quadratic in x” mean?

I'm reading a book on probabilistic robotics and it mentions that "this probability density function is quadratic in x." I haven't heard of the phrase "quadratic in x" before. Can someone explain ...
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1answer
19 views

If $x_1, \ldots, x_n$ have probability distribution function $F(x)$, then the maximum has probability distribution function $F(x)^n$

A random sample $x_1,x_2,.....,x_n$ is taken from a population , which has the probability distribution function $F(x)$ and the density function $f(x)$ . The values in the sample are arranged in ...
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0answers
30 views

Probability of having K cigarettes in one of the 2 packs of cigarettes

We have 2 packs of cigarettes, N cigarettes in each of the pack. We keep taking out a cigarette from those packs randomly, until one of the packs gets empty. How much is probability that the other ...
0
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1answer
80 views

Combinatorics Statistics Probability of a Letter Chain

What formula could help me quantify the probability of a chain of three letters (English Alphabet) where each letter is based on the previous one (stochastic modeling, Markov-chains, probabilities) ...