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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0answers
22 views

extension of log concave functions

So I need to prove something or see if its true and I don't know how to write in nice math text because this is my first question, so please bear with me We have a CDF $F_h(s)$ for $0\le s\le 1$. The ...
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2answers
29 views

Unusual Probability Question

Wheel of fortune: Assume that the probability for an angle φ is P(φ) = λ$φ^2$. The game pays $1000 times the angle. a) What is λ? b) Find the expectation and the variance of the game. Comments: ...
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1answer
22 views

Probability and Combinations Question-Without Replacement.

There are 30 biscuits in a box. 12 are wrapped and the other 18 aren't. If I were to take 4 biscuits without replacement from the box, what is the probability that I take exactly 2 wrapped biscuits? ...
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1answer
23 views

conditional probability on three variables

I was trying to understand the relationship between conditional probability and independence under multi variable circumstance. Now I have the following question. If x,z are independent, y is a ...
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1answer
25 views

Select marbles from two bags containing colored and numbered marbles.

This is a bit of a follow-up to this question. The new question I have is this: You have two bags of 300 numbered marbles of either black or white. They are numbered from 1 to 150 for each color. ...
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1answer
46 views

Flip two coins, if at least one is heads, what is the probability of both being heads?

Quick basic question here to make sure I understand conditional probability properly. You flip two coins, and at least one of them is heads. What is the probability that they are both heads? Now, I ...
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2answers
18 views

Probability of getting at least 3 heads when flipping four coins

Is there a way to solve the problem considering that the probability of getting a head is 1/2 and then calculating $.5^4$ and multiplying $.5^4$ by 4 as there are 4 ways that this could occur?
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1answer
25 views

Probability of Drawing a Card from a Deck (Part 2)

This is a continuation on a question I asked a few years back: Say you have a 60 card deck containing 12 red cards and 48 black cards. After drawing 7 cards, what is the probability you will have 2 ...
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1answer
48 views

Determine whether the dice is biased based on 10 rolls

A casino game has two dice, each with faces numbered $1$ to $6$. One of them is fair but the other is biased such that a $6$ is twice as likely to appear on top as any one of the other faces. ...
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2answers
40 views

Conditional expectation, indication function

I am given that $X,Y$ are independent Bernoulli RVs with parameter $p\in (0,1)$. I am also told $Z=1_{(X+Y=0)}$. I am asked to find $E[X\mid Z]$ and $E[Y\mid Z]$. I can see that the expected values ...
0
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1answer
26 views

Probability of one device among 6 failing

A certain component of an electronic device has a probability of 0.1 of failing. If there are 6 such components in a circuit. What is the probability that at least one fails? This is not a duplicate ...
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1answer
18 views

Working of selections

There are eight finalists in the 400 m athletics at the world championships. Three of the finalists are from the USA, and the others are from five different countries. The rules for allocating a lane ...
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2answers
23 views

Same Arrangements of the word “MINIMUM”

In how many distinguishable ways can the seven letters in the word MINIMUM be arranged, if all the letters are used each time? My attempt: 3!(2!) = 12 ways. M has 3 choices and I has two choices. ...
3
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1answer
24 views

Given that there are 6 married couples. If we select only 4 people out of 12, what is the probability that none of them are married to each other? [closed]

Please, can you help me to solve this? Given that there are 6 married couples. If we select only 4 people out of 12, what is the probability that none of them are married to each other?
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1answer
28 views

Normal Distribution $E(X^4)$?

So I have the Normal Distribution $f(z)=\frac{1}{\sqrt{2\pi}}e^{-z^2/2}.$ I know any $E(Z^{\mbox{ (any odd #)}})$ makes you integrate an odd function thus giving an answer of zero (i.e. $E(Z^1)$ and ...
1
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1answer
14 views

Generalization of the birthday problem with convergence in distribution.

I have independent identically distributed random variables $Y_1, Y_2, ...$ that are uniformly distributed on the set $\lbrace1,2,...,n\rbrace$. I define $X^{(n)}=min\lbrace k:Y_k=Y_j$ for some $ j ...
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1answer
71 views

Cashier has no change… catalan numbers.. probability question

I think this question uses catalan numbers.. but I don't know exactly how to answer it... its not homework or anything but I need to understand how to do it.. I tried drawing up likes for each 5r ...
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2answers
62 views

Expected value with two uniformly distributed random variables

A surveyor wishes to lay out a square region with each side having length L. However, because of a measurement error, he instead lays out a rectangle in which the north–south sides both have length X ...
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0answers
7 views

Simple lower bound for the connective constant of the plane square lattice for self avoiding walks

We know that the connective constant of plane SAW (Self Avoiding Walks) on the square lattice is between 2 and 3. There are very accurate estimations of this constant. It's very easy to see that it ...
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0answers
11 views

proof of a special case of discrete-time tower property

I'm reading a book on stochastic process and the first chapter is about properties of conditional expectation. One of the example the book gives is the proof of a special case of tower property in ...
3
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1answer
35 views

Proof about independent random variables

Let $X_1,X_2,...$ be independent random variables with $P(X_n=1)=p_n$ and $P(X_n=0)=1-p_n$ Show that $X_n\rightarrow 0$ in probability if and only if $p_n\rightarrow0$, $X_n\rightarrow 0$ almost ...
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4answers
50 views

Probability Question: Dividing Groups [closed]

There are 4 boys and 12 girls in a class. They are randomly divided into 4 groups of 4. What is the probability that each group contains a boy?
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1answer
28 views

Probability Generating Functions- Dependent Poisson Distributions

I was wondering if anyone could give me a tip on how to proceed with the following question? Suppose X~Poisson(N), where N~Poisson($\lambda$). What is the PGF of X + N? (Where $\lambda$ is a number) ...
4
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2answers
69 views

Uniform distribution, as a sum of biased Bernoulli trials.

Suppose that the probability of $x=0$ is $p$, and the probability of $x=1$ is $1-p=q$. Consider the random sequence $X=\{X_i\}_{i=1}^{\infty}$. We map this sequence by $C$ to a point in the interval ...
0
votes
1answer
13 views

Sufficiency of $\bar{X}$ in a Binomial$(2,p)$ population.

Let $\{X_1,X_2,...,X_n\}$ be a random sample from a $\text{Bin}(2,p)$ population. Use the definition of sufficiency to show that the sample mean is sufficient for $p$. Here I am not allowed to use ...
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0answers
44 views

Probability in Combination of 5 colour in 9 spaces

We have 5 colours: red, green, blue, black and white, and 9 spaces to paint with only one of that colours each. What is the probability of having 5 spaces in white and the other 4 all in different ...
1
vote
1answer
33 views

Find $ 1 - a^x$, where $x$ is a random variable

I'm trying to find the value of $$ 1 - \left(\frac{99}{100}\right)^N, $$ where N is a random variable given by $$ P(N = i) = \frac{e^{-(i-\lambda)^2 / 2\lambda}}{\sqrt{2\pi\lambda}}, $$ with $0\leq ...
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1answer
41 views

Back to square 1…

A friend of mine was telling me about one of the problems, which he described thus: As you can see, the answer to the toy problem presented here is reportedly 13. However, I don't understand how ...
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2answers
22 views

Posterior probability or Prior probability

I have an arguement with my friends on a probability question. Question: There are lots of stone balls in a big barrel A, where 60% are black and 40% are white, black and white ones are identical, ...
0
votes
0answers
9 views

How we do that to determine the independent variables in data?

I have a data about PM10 (particul matter in air). Now PM10 is my dependent variable and i have to determine that which variables are the best independet variables in my data-set for PM10? I using R. ...
0
votes
1answer
23 views

Show that Kolmogorav's axiom implies that $P(A) \le 1$ for any $ A$

Show that Kolmogorav's axiom $P(A) ≥ 0, P(A ∪ B) = P(A) + P(B)$ if $A\cap B = ∅$, $P(S = 1)$ implie that $P(A) ≤ 1$ for any $A$.
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5answers
40 views

Throw a pair of dice 60 times. What is the probability that the sum 7 occurs between 5 and 15 times?

Throw a pair of dice 60 times. What is the probability that the sum 7 occurs between 5 and 15 times? I know this is how you could calculate the probability of sum 7 occurring 5 times: (60 choose ...
0
votes
1answer
17 views

Bounding $\mathbb{E}(X_{i_1}\cdot \ldots \cdot X_{i_k}) $

Consider random variables $X_1,\ldots X_n$ with zero mean, variance at most $1$, $k$-wise independent $k\leq n $ and bounded: $|X_i|\leq C$ for some $C\geq 1$. If I assume $k$ is even, how can I ...
0
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2answers
28 views

Proving $P(A|(B \cap C)) = P(B | (A \cap C)) P(A | C) / P(B | C)$ using Bayes' theorem.

The following equation can be proven rather uglily, provided that $P(B \cap C)$, $P(A \cap C)$ and $P(C)$ are non-zero, by expanding the conditional probabilities. $$P(A | (B \cap C)) = \frac{P(B | ...
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0answers
38 views

Expectation of product of cosines

I am reading a paper that starts with $$ E[ \cos( a(x-y) ] = E[ \cos(a x) \cos(a y) + \sin(a x) \sin(a y) ] $$ where the expectation is over $a$, then converts it into something of the form $$ = 2 ...
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2answers
39 views

Show $E\left(\mathbf{X}_i \otimes \mathbf{u}_i\right)=\mathbf{0}$ implies $E\left(\mathbf{X}_i^{\top}\mathbf{G}\mathbf{u}_i\right)=\mathbf{0}$

Let $\mathbf{X}_i$ be a $G \times K$ random matrix, and let $\mathbf{u}_i$ be a $G \times 1$ random vector, and suppose we have a sample of $i=1,\ldots,N$ of each. Suppose the following condition ...
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0answers
16 views

pROBABILITY USING DICES [closed]

When dice are irregular so that the sides of the dice are not equal in size or weight, then the most accurate way to determine the probability that they will land with a certain side (such as 5) up is ...
1
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0answers
13 views

inter-event time distribution

We have a counting process N(t) and two processes X(t) and Y(t) where each renewal point of N(t) is a renewal point of X(t) with probability q or Y(t) with probability 1-q. If Fn(t) is the ...
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0answers
12 views

Transition probability of Brownian Bridge

This is homework so no answers please Consider Gaussian $X_i\sim N(0,t_{i}(1-t_{i}))$ s.t. $\frac{X_{1}}{(1-t_{1})}$ and $\frac{X_{2}}{(1-t_{2})}-\frac{X_{1}}{(1-t_{1})}$ are independent (with ...
-1
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0answers
30 views

Probability of upper quartile student

A teacher was asked by her principal to select 7 students at random from her class to take a standardized math test.The teacher previously had rank ordered her students on the basis of their ...
0
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1answer
21 views

Possible/Impossible Probability Question

I'm not sure if there is a question like this already here, but... I just thought of a question related to probability, and I was wondering if it was possible: Suppose you want to ask someone to ...
0
votes
1answer
27 views

probability of teacher selecting students [closed]

A teacher was asked by her principal to select 6 students at random from her class to help out on an outing to a senior's home. In her class, she has 6 girls and 4 boys. The principal believes that ...
0
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1answer
18 views

Expectation under two equivalent probability measure

For two probabilities, if they are equivalent, then does there exist a r. v such that the signs of its expectation under those two probabilities are different?
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1answer
31 views

A gambler who is equally likely to either win or lose one unit

A gambler who is equally likely to either win or lose one unit on each gamble will be down n before being up 1 with probability 1/(n + 1); or equivalently, P(gambler is up 1 before being down n) = ...
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0answers
21 views

Estimate on the Positive probability of not hitting finite measure sets in $\mathbb{R}^{d}$

In $d\geq 3$, we have that BM is transient a.s. i.e. $\lim_{t\to \infty}|B_t|=\infty$. But does this imply $1-P_x(T_A<\infty)>0$ for Borel sets $A\subset \mathbb{R}^d$ with ...
2
votes
6answers
53 views

Expectation of two dice game

The game plays like this: You roll two dices at the same time. If you get same number on both dices, you have to roll again, until you get different numbers. If you get different numbers, you stop. ...
1
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3answers
86 views

In Texas Hold'em poker, is the ranking according to chance of beating 1 opponent's hand the same as according to beating multiple opponents?

In Texas Hold'em poker, you can rank hands according to the probability of beating one randomly generated opponent's hand. However, no one can compute the exact probabilities of beating $8$ random ...
0
votes
1answer
12 views

Bernoulli trials case in probability

A fair die is tossed twice. About how many times would you expect to roll 3 or greater? So based on sequence of Bernoulli trials: P(exactly k successes in n trials) = C(n,k) p^k q^(n-k) where p = ...
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votes
0answers
32 views

probability distribution function of two independent variables

Let $X$ be a random variable whose distribution function is $F_X(t)=3^{-t}$. Suppose that $Y$ is another random variable whose distribution function is $F_Y(t)=4^{-t}$. What is the probability that at ...
1
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4answers
80 views

Expected number of rolls on a dice?

You roll a die until you have seen a 5 on 4 of the rolls (e.g. ⟨5,3,2,5,4,1,6,5,2,5⟩. What is the expected number of rolls this will take? I think that I am way overthinking how I should be going ...