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 ...

learn more… | top users | synonyms (1)

0
votes
0answers
3 views

Probability of 7 Card Hand with All Different Ranks?

Suppose we're dealt a 7 card hand from a standard 52 card deck. I'm trying to find the probability that all 7 cards are different ranks (that is, no two cards share the same rank). I know the ...
0
votes
1answer
13 views

Probability of winning in a coin tossing game

Suppose we have a fair coin. We play a game as follows: $A$ wins if there are 5 heads, $B$ wins if there are 3 tails, and we flip the coin until somebody wins. What's the probability that $A$ wins? ...
1
vote
1answer
15 views

Conditional probability with balls in urns involving discards

I found this problem in a statistics book, and I'm wondering if my solution is correct. "You and a friend play a game involving 20 balls in an urn, of which 1 is red and 19 are white. The game is ...
0
votes
0answers
15 views

Probability: student passing an exam by randomly guessing (no calculator)

Assuming you can't use a calculator, how do you estimate the answer to the following problem? Suppose an exam has 40 questions, all multiple choice. Each question has 5 choices and you need 20 ...
0
votes
0answers
7 views

Expected value of Cumulative Hazard

Define $T=\min(T^0,C)$ where $T^0$ is the failure time and $C$ is the censoring time. Define the failure indicator $$\delta = \begin{cases} 1 & \text{if $T^0\leq C$}\\ 0 & \text{if $T^0> ...
0
votes
0answers
14 views

Can an a.s. (almost surely) finite random variable be a.s. UNbounded?

I thought that if a random variable, $\eta^2$, is assumed to be a.s. finite, then $\eta^2$ must be a.s. bounded. In the Martingale Central Limit Theorem in Hall & Heyde, they assume this: "let ...
0
votes
1answer
19 views

Weighted Coin Toss Probablity

Suppose two weighted coins are tossed. The first is weighted so that it comes up heads with probability $\frac{1}{3}$. The second is weighted so that it comes up heads with probability $\frac{1}{4}$. ...
0
votes
1answer
21 views

Standard Normal Distribution and CDF

I have a data set which consists of measured time in seconds. Secs= ${3000, 3857, 2400, 3323}.$ Mean $\mu =3145$. Standard deviation $\sigma=609.556$. I calculated the Standard Normal variable for ...
1
vote
0answers
16 views

Relationship between Characteristic Function and Eigenfunction

In probability we talk about "characteristic functions" of random variables, usually written as $\Phi_X(t)=E[e^{itX}]$. Is the characteristic function in some sense an "eigenfunction" (a function f ...
0
votes
0answers
7 views

Conceptual question about independence and stopping times

Let $\{X_i\}_{i\in \mathbb{N}}$ be a sequence of i.i.d. random variables with common distribution function $\mu$. Consider a property $A$, such that $\mu(A)>0$. Define $T$ to be stopping time ...
1
vote
1answer
15 views

biased coin flipping

Consider $n$ biased coins such that the probability that heads is flipped is $\frac{i}{n}$ for coin $i$ for $i=1, 2, \dots, n$. If a coin is selected at random, flipped, and shows heads, what is the ...
2
votes
3answers
68 views

What's the probability of a an outcome after N trials, if you stop trying once you're “successful”?

This follows on from this question about being hit by a bus. In this question, there is a 1/1000 chance of being hit and the question was about the probability of being hit if you cross the road 1000 ...
1
vote
2answers
31 views

Probability - selecting n boys and n girls

There are $n$ boys and $n$ girls. One at a time, one of the boys is selected at random. When chosen, the boy selects a girl of his choice. Santiago, one of the boys, wants to choose Mildred. If every ...
0
votes
0answers
17 views

Combining large number of independent probabilities

I am trying to calculate likelihood of laser scan($Z$) at give pose($x$) with known map ($m$) using beam based model $P\left(z_t|x_t,m \right)=\prod_{i=1}^{n}P'\left(z_i|x_t,m \right)$ My scan ...
0
votes
1answer
15 views

$n$-step transition probability of a Markov chain

Let $(X_t)_{t\in\mathbb{N}_0}$ be a time-homogenous Markov chain over a finite state space $\left\{1,\dots,m\right\}$, so that we've got $$\Pr(X_{t+1}=j\mid X_t=i_t,\dots,X_0=i_0)=\Pr(X_{t+1}=j\mid ...
1
vote
1answer
30 views

Help applying Bayes' Law

my problem is the following: Lets imagine we have a computer with 3 memories (m1, m2, m3). When data is needed it is searched if m1, if not found in m1, it is searched in m2 and so on. P(finding ...
7
votes
2answers
988 views

1/1000 chance of a reaction. If you do the action 1000 times, whats the new chance the reaction occurs?

A hypothetical example: You have a 1/1000 chance of being hit by a bus when crossing the street. However, if you perform the action of crossing the street 1000 ...
1
vote
1answer
36 views

How can I calculate $ \sum_{j=0}^{49}\binom{100}{2j+1}p^{100-(2j+1)} q^{(2j+1)} $?

I got the following formula when I tried an exercise in probability: $$ \sum_{j=0}^{49}\binom{100}{2j+1}p^{100-(2j+1)} q^{(2j+1)} $$ where $p+q=1$. These are the "odd" terms in the expansion of ...
0
votes
2answers
25 views

Probability for a 'pair' to occur when rolling 5 dice

5 fair dice are rolled. A pair is defined to be any number that shows up twice, while the rest of the dice show different numbers (to the number on the pair and to each other). I am looking for the ...
-5
votes
2answers
21 views

In a class of 30 students, 5 will be chosen. In how many different ways can delegation be chosen? [on hold]

In a class of 30 students, 5 will be chosen to go to the state capitol on a trip to represent the school. In how many different ways can delegation be chosen?
2
votes
1answer
31 views

Expected Value on code

I'm trying to figure out the expected number of times this algorithm will print. I'm stuck on how to go about doing so. I used an indicator variable to keep track of the number of print statements ...
0
votes
0answers
13 views

Karhunen Loeve representsiton of Ising Model

I was wondering if there is a Karhunen Loeve-type of representation for an Ising random process? In truth I would be really happy to learn about work in KL series for any type of spatial random ...
2
votes
0answers
55 views

Help with conditional probability problem? (With my own attempt first)

I was doing a question today and couldn't understand the answer. Here's the question, my attempt, and the answer: Question In a game of Scrabble, Dalene has the seven letters A, D, E, K, O, Q and ...
0
votes
1answer
10 views

maximum-likelihood: a sequence of events described by a Bernoulli distribution

I am having quite some troubles with the following homework: In a city it's measured for the whole year whether it rained or not. A distribution $\textrm{Bernoulli}(r_t|\rho)$ characterizes the ...
0
votes
1answer
18 views

Probability Independence

I learned at school that to visualize two events A and B as independent, I could interpret event A and B as a Venn Diagram where the two circles are disjoint. If they overlapped the events are ...
0
votes
1answer
35 views

I have 3 random numbers orders - how to find the probability of one of them being the largest?

I have 3 random numbers (not integers) and all I know is the probabilities of: number 1 to be larger than number 2 $= p_{12}$ number 1 to be larger than number 3 $= p_{13}$ number 2 to be larger ...
1
vote
1answer
25 views

Using the inverse Gaussian integral to find percentiles

I need some help with the following: Let $$R=\mu+\sigma*\epsilon \hspace{1cm} \epsilon \sim N(0,1)$$ I want to argue that $$ \mu + \sigma*\Phi^{-1}(u)$$ are the percentiles of the model when ...
1
vote
1answer
18 views

Cumulative probability of Chi-squared distribution

If $X$ is distributed $\frac{\chi_{10}^2}{10}$ , find the probability that $X > 1.83$ The formula for the Chi-squared CDF I'm using is the following, which is the integral of the PDF formula: ...
0
votes
1answer
13 views

Finding probability given mean and standard deviation

I don't know how to approach this problem: X is normally distributed with a mean of 200 and a standard deviation of 10. Find P(X ≥ 203)
0
votes
1answer
51 views

What is the probability the best case occurs? (Comp Sci Type Question)

I'm having trouble figuring out what's the probability the best case occurs? It's my first time bringing together probabilistic knowledge into computer science. The question goes as such. Consider ...
0
votes
2answers
39 views

Probabilities and random variable problem

Suppose we have a random variable X, and we are given the numerical values of its expectation as well as its s.d. (standard deviation). How can I go about finding the maximum value the probability of ...
2
votes
1answer
26 views

Pig Wheel question

A friend of mine was playing the bar game Pig Wheel recently and posed some interesting questions to me. He was playing with others as a group of four and, acting collectively, they came out about ...
0
votes
0answers
25 views

Problems with convergence in mean

I hope you can help me with the following problem Let $\{ e_i : i\in \mathbb{Z}\}$ be and independent U.I. sequence of scalar random variables with zero mean. Let $\{ A_j : j \geq 0\}$ be a sequence ...
0
votes
0answers
14 views

Cesaro means converges in first mean to 0.

I would appreciate any suggestions to prove the following statement If $\{ X_i: i=1,..\}$ is a sequence of independent uniformly integrable (U.I) random variables ...
2
votes
1answer
43 views

How can I simplify $ \sum_{r=0}^{m-1}r^3\frac{\binom{m}{r}(m-r)!\begin{Bmatrix} n\\ m-r \end{Bmatrix}}{m^n}$?

Let $N$ and $M$ be sets with $n$ and $m$ elements respectively with $n>m$. Randomly assign a function $f:N\to M$. Suppose that the probability of each element in $N$ being assigned to any ...
-3
votes
3answers
37 views

stuck on probabilty question [on hold]

Two technicians are discussing the relative merits of two rockets. One rocket has two engines, the other four. The engines used are all identical. To ensure success the engines are somewhat redundant: ...
0
votes
2answers
32 views

Let $X_{1},X_{2}, \dots, \sim Exp(1)$ i.i.d. - Calculate the probability of $P[\max{(X_{1},\dots,X_{n},)} < \log(n) - 5] $ for $ n > e^{5}$

Let $X_{1},X_{2}, \dots, \sim Exp(1)$ i.i.d. - Calculate the probability of $P[\max{(X_{1},\dots,X_{n},)} < \log(n)-5] $ for $ n > e^{5}$ as well as $n \rightarrow \infty $ The correct ...
0
votes
1answer
33 views

Finding probability of a student passing

A student took his final exam. He took 3 subjects: Math, English and Science. The grade can be 0-7 for every subject. And if his grades sum up to atleast 10, he pass. However, if he scored 1 or 0 on ...
2
votes
1answer
36 views

How to calculate Full joint probability distribution

This is a past exam question, I did it wrong in the exam, I'm reviewing it right now. The question is to compute the full joint probability of the problem below: I draw the full joint ...
1
vote
1answer
23 views

raBinomial distribution with dependent trials?

I need your help with following problem: String with n characters is given. For each character in string there is probability p that it is wrong. Now you take a sliding window of length k, k<= n, ...
-2
votes
1answer
21 views

Simple question probability [on hold]

I am facing the following problem: The chance of finding data in the first memory is 0.8. If we dont find it in the first memory we go to the second memory. The chance of finding data in the second ...
-2
votes
0answers
21 views

Coin tossing probability question [on hold]

The question is as follows: "Let X be the number of coin tosses until heads is obtained. Suppose that the probability of heads is unknown in the sense that we consider it to be a random variable ...
1
vote
1answer
21 views

How to estimate the mutual information

I have two discrete non-negative random variables $X$ and $Y$. I know $X$ is the number of heads you get by tossing $n$ unbiased coins and I know $Y$ is in the range $0,\dots n$. I can sample from ...
2
votes
1answer
21 views

A question involving the probability generating function

I'm stumped by the following exercise: The probability generating function for X is given by $g_{X}(t)$. What is the probability generating function for $X+1$ and $2X$, in terms of $g_{X}(t)$? For ...
2
votes
1answer
55 views

Convergence in distribution of a sequence of random variables

Let $Y_1,Y_2,...,$ be independent $C(0,1)$ random variables, determine the limit distribution of : $Z_n = \dfrac{1}{n} \cdot max\{Y_1, Y_2,..Y_n \} $ as $n \rightarrow \infty $, Here is my approach: ...
5
votes
4answers
409 views

Coin tossing question [duplicate]

Adam, Bertrand, and Carissa toss a coin in sequence until one person wins by tossing the first head. If the coin is fair, find the probability that Adam wins. Can somebody tell me if I'm on the ...
0
votes
3answers
51 views

Need help with flaws in statistical reasoning

The problem is as follows - there are three couples and six chairs in a row. The six individuals are seated at random. What is the chance that at least one couple will be seated together? Here's my ...
0
votes
1answer
29 views

Probability of each outcome from dice notation

In the "dice notation", XdY means you rolls X number of Y-sided dices, and adds the results together to get the final outcome. For example, on 3d3 distribution, you can get number from 3 to 9, and ...
0
votes
1answer
28 views

Large deviation theory for square of variable?

Let $X_n$ be a sequence of iid $N(0,1)$ random variables. Find the approximate value of $P(X_1^2+X_2^2+\dots+X_n^2 >= 2n)$ when $n$ is large. Use large deviation theory. I have tried but failed to ...
0
votes
0answers
30 views

Showing that P$_X$ is a probability.

I have a question about a exercise, where I have to show that $P_X (D)$ is a probability, where I have to show four cases. We say that $X$ is a r.v. with the space $\mathcal{D}$. If ...