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
1answer
24 views

Ordered Partitions

I'm having trouble figuring out exactly how one would get the answer for a question such as: "how many ways can 9 concert tickets be divided between 4 concertgoers, such that one person receives 3 ...
1
vote
1answer
26 views

A question about probability (1)

Given a circle $C$ of radius $a$, a point is selected at random within the circle, what is the probability that the point is the centre of the circle?
8
votes
1answer
129 views

If half the population were murderers, and they could only kill once, how many would survive?

So here's the rules: Half the population are murderers Each murderer can only kill once We assume the nobody will fight back, and only murderers can murder Murderers can kill other murderers Only ...
38
votes
1answer
991 views

Does a randomly chosen series diverge?

Pick a point at random in the interval $[0,1]$, call it $P_1$. Pick another point at random in the interval $[0,P_1]$, call it $P_2$. Pick another point at random in the interval $[0,P2]$, call it ...
2
votes
1answer
35 views

probability with replacement

A box contains 4 red, 3 black and 2 white cubes. A cube is randomly drawn and has its color noted. The cube is then replaced, together with 2 more of the same color. A second cube is then drawn. ...
2
votes
1answer
99 views

a generalization of normal distribution to the complex case: complex integral over the real line

How to prove $\int_{\mathbb{R}} e^{-\frac{(x+it)^2}{2}}dx=\sqrt{2\pi}$ for any $t\in \mathbb{R}$? I only obtained the case that $t=0$, $\int_{\mathbb{R}} e^{-\frac{x^2}{2}}dx=\sqrt{2\pi}$. Thanks.
0
votes
1answer
31 views

Truth Tables. (If Q, then P)

Suppose people from Tracy always tell the truth and people from Livermore always lies, You meet Diego and he says,' If I came to San Jose on the train, then I am from Livermore ."is it possible ...
0
votes
1answer
7 views

Decomposition of chance constraint optimization problem

I want to decompose a chance constraint optimization problem and the constraint is: $Pr\left( \sum_{i}^{}{\left( x_{i}+\xi _{i} \right)}\leq c \right)\geq 1-\epsilon $ where $\xi _{i}$ are ...
0
votes
3answers
151 views

How to put probability density function in C++?

I have a random variable X that has a probability density function of f(x)=x^(-1/2)/2 for all x between 0 and 1. double RANDOM; I need to give a value to RANDOM, that accepts the PDF All that I ...
1
vote
1answer
21 views

Probability of zero events in large population given known event rate

I have a group of 1444 patients that have been included in a group of different trials. The trials found that none (zero) of the patients had a specific complication (independent). The known incidence ...
0
votes
2answers
1k views

Flip a coin 6 times. What is probability of at least 4 heads?

I can figure out the much simpler case of the probability of getting at least 2 heads in 3 coin flips: There are 8 (2^3) ways to flip a coin 3 times: HHH, HHT, TTT, TTH, HTH, HTT, THT, THH. 4 of these ...
0
votes
1answer
28 views

Fair coin tossed $3$ times. $X$ is # of H's on $1st$ and $2nd$ tosses, $Y$ is # of H's on $2nd$ and $3rd$ tosses. Write Joint PD.

Suppose a fair coin is tossed $3$ times. Let the random variable $X$ represent the number of heads on the first and second tosses and let $Y$ represent the number of heads on the second and third ...
2
votes
2answers
58 views

Probability question - (Probably) Bayes' Rule and Total Probability Theorem

I just took a probability final exam and was fairly confident in my solution of 28/31, but I wanted to be sure... because according to ...
0
votes
0answers
28 views

Interesting Probability Game With Uneven Return Scenarions

Let say we play a game. The game which spans the course of 5 trials. The game is as follows. You either receive 100 points or 40 points as a final payout. The only time a payout of a 100 points occurs ...
0
votes
0answers
31 views

Random permutation with a scientific calculator

I have 8 people whom I want to divide into 2 groups. The allocation must be uniformly at random, i.e., every person must have equal probability of joining either group. We came across a situation ...
1
vote
1answer
25 views

Distribution of $U + Y$ $\mod 1$

Let $U$ ~ Unif$[0,1]$ be uniformly distributed on $[0,1]$. Let $Y$ be some random variable, independent from $U$. What is the distribution of the random variable defined as $X=U+Y \mod 1$? Can ...
0
votes
0answers
38 views

Girsanov Measure Question.

If $Z_t = exp^{\int_0^t X_s dW_s - \frac{1}{2} \int_0^t (X_s)^2 ds}$ is a martinagle then by Girsanov's theorem, the measure $P_T$ defined by $P_T(A) = E^P(AZ_T)$ is mutually absolutely continuous ...
0
votes
1answer
28 views

Dealing with this random variable problem

$X_1,X_2,X_3,\ldots$ are IID random variable taking values in $(-1,\infty)$. Also $t\in(0,1)$. $f_1>0$ is a positive constant and $f_2,f_3,f_4\ldots$ are positive functions of one variable. ...
0
votes
1answer
34 views

Log-space probability of a log-space probability not occurring

Normally the probability of some probability $p$ not occurring would be $1-p$. However, I'm working with very small probabilities and therefore must work with $p$ in $\log$ space (Ie. I'm working with ...
1
vote
1answer
20 views

Computing expectation by conditioning

A coin is tossed as long as it shows heads. Let $X$ be the number of heads before the first tail. After that you throw a dice $X$ times. Let $Y$ be the number of sixes. calculate $E[Y]$ I've ...
1
vote
3answers
76 views

Probabilities When we use the Combinations and when not? nCk vs nPk

Question 1: I am working on probabilities and on some exercises the solutions either use the nCk or just n. I want to find a method to understand when I have to use the nCk and when not to. Example ...
5
votes
3answers
153 views

Expected value of number of draws

We have $5$ number in a bag: $(1,3,5,7,9)$. We draw one from the bag and then put it back. We do this until the sum of the numbers can be divided by $3$. Whats the expected value of the number of ...
2
votes
1answer
26 views

Broken trucks at a road

If three trucks break at locals random distributed of a road with lenght $L$, find the probability that $2$ of those trucks are not at a greater distance than $d$, fot $d \leq \frac{L}{2}$ My ...
1
vote
0answers
18 views

Expected number of errors in a magazine page

The expected number of typographic errors in a page of a certain magazine is 2.What is the probability that an article of 10 pages has 2 errors? My attempt: I thought that if $X$ is the r.v that ...
1
vote
1answer
82 views

CDF of a continuous random variable with discontinuity

With a piecewise PDF defined as $$f(x)=\begin{cases} 1/2 & -3 < x < -2 \\ e^{-2x} & x>0\end{cases}$$ Would the CDF of this function between $-2$ and $0$ be $0.5$, even ...
0
votes
1answer
106 views

Poisson distribution, (conditional) probability question

Suppose Bob receives on average one call per night from his father. Find the probability that 7th January was the third night this year (starting on 1st January) when no night calls were received. I ...
0
votes
1answer
34 views

Probability with same number of heads and tails

I have this question that I don't know where to begin, any help will be greatly appreciated. Consider the following random experiment. Toss a coin until the same number of heads and tails have been ...
1
vote
1answer
33 views

Solving a general integral (expectation of some variant of exponential distribution)

Suppose $X$ is distributed exponentially with parameter $\lambda$. Its pdf is $\lambda e^{-\lambda x}$, and the calculation of its expectation is straight forward: $\mathbb{E}(X) = \int_0^\infty ...
0
votes
2answers
42 views

Binomial and Normal Distribution Problem - Check solution

Whooping cough is a highly contagious bacterial infection...About 80% of unvaccinated children who are exposed to whooping cough will develop the infection, as opposed to only about 5% of vaccinated ...
0
votes
1answer
48 views

Continuous probability about meeting between two friends [duplicate]

My friend and I are hoping to meet for lunch. We will each arrive at our favorite restaurant at a random time between noon and 1 p.m., stay for 15 minutes, then leave. What is the probability that we ...
0
votes
1answer
23 views

Question regarding Poisson random variable

I'm reviewing a question I did for the Poisson random variable and I can't remember how I got the the answer to part b). The problem goes as follows: "Suppose that the number of typographical erros on ...
0
votes
3answers
34 views

Probability of having less than 3 females if…

Assuming that half the population is female and assuming that 100 samples of 10 individuals are taken, how many samples would you expect to have 3 or less females? Can someone please ...
1
vote
1answer
16 views

Normal Distribution how $N(x-x_n|0,\sigma^2) = N(x |x_n,\sigma^2) $

I read an expression Could someone explain the step $N(t-t_n|0,\sigma^2) = N(t | t_n,\sigma^2) $ ?
-2
votes
1answer
88 views

find probability of people sitting in a circle in a particular manner [closed]

There are 12 people sitting in a circle. what is the probability that exactly 3 people sit between A and B?
0
votes
0answers
40 views

If $A=\{R_1\le\frac{1}{2}\}$ and $B=\{R_2\le\frac{1}{2}\}$, find $P(A\cup B)$

Let $(R_1, R_2)$ have the following density function $f_{12}(x,y)=\cases{ 4xy & \text{if } 0\le x,y\le1, x\ge y\cr 6x^2 & \text{if } 0\le x,y\le1, y>x }$ If ...
0
votes
1answer
24 views

Risk Faced With Insurance

I'm studying a simple models of insurance. Suppose that a machine breaks down with probability $p$, and suppose that an insurance company collects enough in premiums to pay for $k$ breakdowns. What ...
0
votes
1answer
31 views

Probability and set notation.

Suppose that the probability that the Dow-Jones stock index increases today is $.54$, that it increases tomorrow is $.54$, and that it increases in both days is $.28$. What is the probability that it ...
1
vote
1answer
23 views

Random variable sum

Let $X$ be random variable representing square of number that fell on die, and $Y$ random >variable which is $-1$ if number on day is less or equal to $4$ and $1$ otherwise. Find distribution of ...
1
vote
3answers
135 views

Question regarding basic probability.

I'm looking for confirmation that what I for did this question is correct: "If two people are randomly chosen from a group of eight women and six men, what is the probability that (a) both are women ...
1
vote
2answers
87 views

Is expectation countably additive?

I am supposed to prove that Let $X \ge 0$ be a random variable defined on $(\Omega, \mathcal{A}, > P)$ and $\mathbb{E}[X] = 1$. Define $Q: \mathcal{A} \to \mathbb{R}$ by $Q(A) = ...
1
vote
1answer
59 views

Exercise of probabilities [closed]

I have difficulties with this problem. I will appreciate some help of you. Thank you. A printing machine capable of printing any of $n$ characters $a_1, . . ., a_n$ is operated by electrical ...
0
votes
1answer
36 views

How to rewrite this logarithmic update rule

I tried to rewrite the equation given below. I get stuck getting rid of the $ P(n|z_{1:t})$ on the left side. How can this be done? $$ P(n|z_{1:t}) = \left[1+ \frac{1-P(n|z_{t})}{P(n|z_t)} ...
1
vote
0answers
38 views

Probability Homework Puzzle

A box 1 contains 5 white and 6 black balls. Another box II contains 6 white balls and 4 black balls. A box is selected at random and then a ball is drawn from it. (i) What is the probability that the ...
0
votes
2answers
27 views

Probability puzzle

Find the probability of drawing 4 white balls and 2 black balls without replacement from a bag containing 1 red, 4 black, and 6 white balls. My logic is ...
0
votes
1answer
14 views

Find moment generating function given rth moment without Laplace

Let W be a random variable. Given the rth moment, $E(W^{r}) = \frac{r!+6^{r}}{2^{r}} = M_w^{(r)}(0)$, $r \geq 0$, how does one derive $f(w)$? I know that $M_w(t)=E(e^{wt}) = \begin{cases} ...
0
votes
0answers
313 views

How can I derive the PDF from conditional probabilities?

I have some function $P(i)$ which is the probability of success for an experiment on the $i$th trial. The probability mass function for the first successful trial is: $$PMF(n) = \left( ...
1
vote
1answer
32 views

Probability question and how to approach it

Nine tiles are numbered 1, 2, 3, . . . , 9. Each of three players randomly selects and keeps three of the tiles, and sums those three values. Find the probability that all three players obtain an ...
2
votes
1answer
50 views

Square Line Picking

The probability density function of the distance between two points chosen randomly on the unit square is given by: $ P(\ell) = \begin{cases} 2\ell\left(\ell^2 - 4\ell + \pi\right) & 0 \leq \ell ...
0
votes
0answers
14 views

Trouble with Largrange Multipliers and expectation.

I am reading the following argument: Maximize $E[Log(X(T))]$ subject to $E[Z(T) X(T)]=x$, where $X(T),Z(T)$ are random variables, $x$ is a constant, and E is expected value (You can read this as ...
5
votes
5answers
135 views

Choosing something of $0$ probability

First of all, i am only a newbie and i am pretty sure that my thinking is faulty somewhere, so along the way as i explain things i will probably say something with an error and i hope you will help me ...