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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18 views

Expectation of squared Ito integral

Let $\omega$ be a standard Brownian motion. How do you compute the expectation involving the square of an Ito integral: $ ...
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1answer
35 views

Probability confusing question

I saw this in my probability class past exam papers I saw the answer key but I still can't fully understand. I wish somebody can walk through this with me :) A company takes out an insurance policy ...
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0answers
20 views

Exponent - Solving for an unknown within an expectation

I have reached a stage where I need to solve for an unknown number, $\theta$ . However, I stuck and don't know how to proceed further. The equation to be solved is: $E\left[ \exp(\theta a^i) * ...
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0answers
16 views

The independence of 3 positive events [on hold]

Let $A, B ,C$ be 3 positive events. Suppose $A$ is independent of $B$ and $B$ is independent of $C$. Does $A$ independent of $C$
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0answers
8 views

Calculate the pdf from covariance matrix

I tried to solve the following problem: mu,C are mean vector and covariance matrix of three-dimensional Gaussian random vector X. C(3x3) , mu(3x1). And Y=AX+b where A is 2x3 matrix , b: 2x1 vector ...
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0answers
10 views

Relevant Distribution

I have a 7 year data set with revenue, revenue growth percentage, ebitda liabilities and assets. I have been asked to find the underlying relevant distribution used in the above data set. I'm drawing ...
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1answer
11 views

Expected value of characteristic function

I was wondering about the expected value of the characteristic function $\chi_A$ for some set $A \in \mathcal{A}$ in a probability space $(\Omega, \mathcal{A}, \mathbb{P})$. It should be ...
3
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0answers
46 views

The Lost Boarding Pass Advanced

The Lost Boarding Pass is a famous puzzle as follows: On a sold out flight, $100$ people line up to board the plane. The first passenger in the line has lost his boarding pass, but was allowed in, ...
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1answer
21 views

Calculating the distribution of a compound random variable

Given $X\sim U(1, 0)$ and $Y\sim Exp(1)$, determine the density function of $Z:=\frac{X}{Y}$. Now, without looking up how to do it I tried to figure it out myself. The value of the density function ...
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0answers
10 views

Statistical uncertainty on a percentages inferred from an A/B test

Question: What is the statistical uncertainty on percentages inferred from an A/B test? Example: $N = 100$ people are presented with an A/B choice (e.g., jumping into shark-infested water, choosing ...
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0answers
20 views

Chi-square test of independence: show that sum of squared standard normals has chi-square distribution

I'm studying the chi-square test of independence. According to my understanding, we first hypothesize independence between variables and consider them as being normally distributed. Then we go on to ...
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0answers
18 views

Probability Question Simple Qns

Assume each of the four users is active for 20% of time and data generation rate of the four users are 400kbps, 600kbps, 700kbps and 800kbps, respectively. Calculate the probability that the data ...
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1answer
11 views

Coversion of Probabilities based on time

QUESTION If a shooting star has an 80% chance of appearing in the next hour, what is the chance of it appearing in the next half hour? How does one go about finding probabilities such as this? ...
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2answers
46 views

Probability of a double-headed coin

Here are three related problems from Blitzstein and Hwang's Introduction to Probability. Curious if my approach is sound. I'm reasonably confident in the first result, but not so much in the other ...
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0answers
7 views

“Distance” of iid gaussian variables

Take two i.i.d. Gaussian R.V.s $X$ are $Y$ both of which are $~N(0,a\sigma)$. Define a new R.V. $D = \sqrt{X^2 + Y^2}$. What's the expected value $E(D)$? In researching this I'm seeing references ...
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0answers
10 views

Definition of rough path

There are many books and notes on the rough path theory. A rough path is defined as an ordered pair $(X, \mathbb X)$, where $X$ is a path mapping from $[0, T]$ to some Banach space $V$ and $\mathbb X: ...
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3answers
24 views

Cricket Probability question

My understanding of probability is little weak, and it was since high school I am struggling with it.This question struck me yesterday while watching IPL. ... In a normal game of cricket, there are ...
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0answers
13 views

Bayesian Estimation of the mean of a multi-variate Gaussian

The posterior mean of a multivariate normal distribution is to be estimated with the Bayes rule for densities (http://www.math.uah.edu/stat/dist/Conditional.html), following the approach as described ...
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1answer
12 views

Joint distribution function from marginals

Is it possible to obtain joint distribution function when only the marginal distribution functions of random variables are given and, the random variables are not independent? If possible, it would ...
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0answers
30 views

PROBABILITY PROBLEM PLEASE HELP ASAP [on hold]

if you selected the numbers 1,2 ,3 and 4 at random. That is you selected then in some way so that each number was equally likely to be chosen- what is the probability of getting a fraction sum that ...
2
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2answers
20 views

Probability of sorting at least one correctly

If I have 5 balls label 1 through 5, to put one in each of 5 boxes also labeled 1 through 5. What is the probability of putting at least one ball in it's matching box? My first approach was to ...
0
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0answers
13 views

Conditional expectations with identical marginals and positively dependent but unknown joint distribution

Let $A$ and $B$ be random variables, each with marginal distribution $% U\left( 0,1\right) $, but unknown joint distribution $H\left( a,b\right) $. Suppose $A$ and $B$ are each stochastically (weakly) ...
0
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2answers
18 views

Joint Probability density function

Two components in rocket operate independently and the probability that each component fail is p. Let X denote the number of launches require to have a failure of component 1 and Y denote the number ...
2
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2answers
26 views

Can there exist $3$, $4$ and $5$-faceted shapes with congruent flat sides in $\mathbb{R}^3$?

I rose this question in my discrete math class (the unit on probability) not too long ago. For instance, a two-sided shape (like a coin) can be one with any geometrical shape as its "side," such as a ...
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1answer
19 views

Conditional probability distribution notation versus conditional probabilities of a single sample space?

When writing conditional marginal probabilities, the following seems to be the notation: $$p_{i|Y=y_{j}} = P(X=x_{i}|Y=y_{j}) = \frac{P(X=x_{i},Y=y_{j})}{P(Y=y_{j})}=\frac{p_{ij}}{p_{+j}}$$ This is ...
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0answers
35 views

Expected costs, benefits of a test [on hold]

The president of a firm in a highly competitive industry believes that an employee of the company is providing confidential information to the competition. She is 90% certain that this informer is the ...
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0answers
12 views

Unbiased estimator for geometric distribution parameter p

I believe that the MLE of parameter $p$ in the geometric distribution, $\hat p = 1/(\bar x +1)$, is an unbiased estimator for $p$ and would like to prove it. So far, I have: $E[\bar x + 1] = E[\bar ...
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1answer
23 views

which choice is better?

Lets say you were writing a program to play checkers. Im simplifying the numbers, but the gist should be obvious. Your program calculates the odds of Move A to have a 100 chances to win the game and ...
0
votes
2answers
48 views

Probability of segment lying in circle

Given a circle of radius R: $x^2+y^2\le R$, find probability of horizontal segment with length $\frac{R}{2}$ lie whole inside this circle. Position of segment's center has uniform distribution in ...
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0answers
25 views

Markov Chain problem application

Let $P$ be the transition matrix for a regular Markov chain and $v$ be its equilibruim vector. Show that $v$ has zero entries. How would you prove this? I am struggling in this class. Any help is ...
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0answers
60 views

Random walk, expectation & variance, joint probability, approximation question [on hold]

Consider the following random walk on a plane: The walk commences at the origin and at each timestep, a step of unit length is taken in a random direction $\theta$ (measured relative to the positive x ...
0
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0answers
9 views

(Empirical likelihood method) Find the order of a parameter given a set of constraints

Firstly we assume that $X_1,...X_n$ are order statistics($X_i\leq X_{i+1}$) from an i.i.d sample of random variables and let $r$ be integer and $r\geq1$. Start with the equation (1) \begin{equation} ...
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1answer
31 views

Expected value with negative exponent

I am trying to solve identify the expected value of a statistic that involves a fraction. I have simplified the expression to: $E[\frac{1}{1+ \sum_i x_i}] = E[\frac{1}{1+ T}]$ However, I am not sure ...
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1answer
18 views

Doubtful answer for conditional probability question

There's a traffic light in a city which works properly, but sometimes it is faulty. If it functions properly today, there is a 95% chance that it will not malfunction tomorrow. However, if it is ...
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0answers
37 views

Expected number of rolls on a 200 sided die to roll a 1? [duplicate]

We have a 200 sided fair die with faces numbered 1 through 200 and want to know how many rolls are expected to roll a 1. How would I go about calculating this?
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2answers
40 views

what is the meaning of probabilities P(A − B)?

Let $A$ and $B$ be two mutually exclusive events. What is the meaning of $P(A − B)$?
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1answer
24 views

Sum of two uniform independent random variables

I would like to find the cdf of $Z=X_1+X_2$, with $X_1\sim U(0,1) $, $X_2\sim U(0,2)$ I always prefer to find the cdf instead of the pdf with convolution, and this time I am having troubles with the ...
2
votes
1answer
32 views

How many seven digit numbers with distinct digits contain a $3$ but not a $6$?

How many $7$-digit numbers with no repeated digits contain a $3$ but not a $6$? The number does not start with zero. $$7 \cdot P(8,6) = 7 \cdot 20160 = 141120$$ because $3$ can be in $7$ positions, ...
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1answer
35 views

Approximating a joint pdf using normal density of two independent variables

I know that given these two random variables (which correspond to the $x$ and $y$ coordinates of a random walk after $n$ steps, their joint probability density function can be $approximated$ by a ...
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votes
1answer
43 views

If $X_n\rightarrow X$ in mean square, then $\mathbb{E}(X_n)\rightarrow \mathbb{E}(X)$ [on hold]

How do I show that if $X_n\rightarrow X$ in mean square then $\mathbb{E}(X_n)\rightarrow \mathbb{E}(X)$ using the Cauchy-Schwarz inequality?
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3answers
21 views

Algebraic simplification of likelihood ratio

Can someone help me understand how this: ...
0
votes
1answer
27 views

Probability Question using Poisson distribution

On average, an employee receive 25 emails each day, of which 60% are ‘spam’. What is the probability that the employee will receive exactly 15 ‘spam’ emails tomorrow? My methodology is such: $$ ...
0
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0answers
27 views

Calculate P(X=Y)

I have a question that asks me to calculate $P(X=Y)$. The probability is based on $4$ trials of a binomial experiment. I was given the $pmf$ of $X$ in the following table: $$\begin{array}{c|c|c|c|} ...
0
votes
1answer
26 views

Probability of choosing a combination [on hold]

A person has $8$ red pills and $8$ blue pills. He chooses $8$ pills at random. What is the probability that the chosen pills are $4$ red and $4$ blue?
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0answers
28 views

Simple Probability of Playing Cards

An ordinary deck of playing cards has four suits: hearts, spades, diamonds, and clubs. Suppose you have a reduced deck of eight playing cards, consisting of four aces and four kings. I draw two cards ...
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1answer
23 views

Probability Another Playing Card question — twist

I completely understand the questions of probability of drawing 2 cards without replacement -- getting a heart or a face card. I add the probability of getting a heart with probability of getting a ...
2
votes
1answer
57 views

Is this chain irreducible and/or Aperiodic? What is its equilibrium mass function?

Consider a Markov chain with outcomes $\{0,…,n\}$ and transition probabilities $P_{i,i+1}=p$ $P_{i,i−1}=q$ for $1\le i\le n−1$ and $p+q=1$. Assume also that $P_{0,1} = P_{n,n−1} = 1$. Is this chain ...
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1answer
47 views

probability, random walk, Markov chain question

Let $P$ be a transition matrix for a regular Markov chain and let $w$ be it’s equilibrium vector. Show that $w$ has no zero entries.
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3answers
72 views

finding the probability to get a diploma

For getting a diploma a person needs to go to $3$ interviews at $3$ teachers: $A,B,C$. In each interview a teacher can give a positive opinion or negative opinion. The person will go to interview at ...
1
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1answer
13 views

Probability function and distribution - taking out fish from a pool

In a pool of fish there are 4 fish of type A, 3 fish of type B, 2 fish of type C, 1 fish of type D. We take out fish without returning them until we get fish of type C for the first time. ...