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)

1
vote
1answer
22 views

Conditional Probability HW Question Semantics

I have a question related to the wording of a basic probability problem which I have partially completed. Specifically, I have trouble wrapping my head around the English statement highlighted in bold ...
1
vote
1answer
88 views

Limited Edition - How many C(6, 3) do I need?

A limited edition of products came out, with sets of 3 items pulled randomly from the series of 6 and sold in 3-packs. I know that C(6, 3) = 20 different possible outcomes, but I'm having trouble ...
0
votes
2answers
49 views

Probability/Set theory problem

The problem is: In some country, there are 3 newspapers. 20% of the population read newspaper A, 16% read B, and 14% read C. 8% of the population read both A and B, 5% read A and C, and 4% ...
0
votes
1answer
54 views

prove this inequality related to probability and information theory

How do I prove this? I'm thinking I should use Jensen's inequality somehow. $$\sum_K p_k(1-p_k) \le -\sum_K p_k\log p_k$$ The assumption that $\sum_K p_k=1$ holds.
0
votes
2answers
30 views

Number of times an experiment must be run, with conditional probability

In a given experiment, event $A$ has a probability of $1.26\%$ of occurring. That is, $P(A) = .0126$. If event $A$ occurs, then event $B$ has a $.99\%$ chance of occurring. That is, $P(B|A) = ...
1
vote
0answers
11 views

Periodicity and Stationarity

Let $g$ be a $f_0$-periodic function and let $V\sim\mathcal U(0,f_0)$. Suppose in addition that $X$ is a stationary process independent of $V$. I've been told that for all $a$, the process $Y$ ...
0
votes
1answer
30 views

How can I answer this question about probability? [on hold]

two basketball teams A and B compete for the championship final in a series of up to seven games. The probability of winning is the same for both teams. Determine the probability that: a) there is ...
0
votes
1answer
11 views

$U\sim \mathcal U(0,a)\overset{?}{\implies}U-\lfloor U \rfloor \sim \mathcal U (0,a-\lfloor a \rfloor$)

Suppose $U\sim \mathcal U(0,a)$ for some $a>0$. Is it true that $U-\lfloor U \rfloor \sim \mathcal U (0,a-\lfloor a \rfloor$)? How can I prove this? If $a\in \mathbb N$ then the following ...
0
votes
0answers
18 views

why is it true that a bunch of sets that are independent are equivalent to sets that can be either itself or its compliment?

I have sets $A_{i1},A_{i2},....,A_{ik}$ where $i$ is a subset of {1,2,3,...,n} representing indices and only k are selected from a total possible n indices. I have sets ...
1
vote
1answer
35 views

conditional probability - conditioned twice

Let $p(\cdot)$ be a discreet probability function and $A,B,C$ be events. What does $p(A|B|C)$ mean? Is this the same as $p(A|B,C)$ or is it: if we treat $D=A|B$ as another event, $p(D|C) = ...
0
votes
0answers
46 views

Mean distance between two points in a disk

Two points(say X_1, X_2) are uniformly distributed in a disk(say disk1) of radius 2r with origin as center. I need to get mean distance of the two points from origin, with the following conditions ...
2
votes
3answers
122 views

Odds for randomly assigning a men-only group in a team working assignment

We are partitioning a group of $30$ people in $5$ groups of $6$ persons each. We have $13$ women and $17$ men in those $30$ people and randomly drawing those people gave us a men-only group. What are ...
0
votes
1answer
25 views

Say (X,Y) has the distribution on the area shown below find P(X>1|Y=1/2) [on hold]

Say (X,Y) has the distribution on the area shown below, find P(X>1|Y=1/2)
0
votes
1answer
23 views

Rolling a d20 dice, dnd mecanics related

lets say i'm rolling a d20 dice i need to get a 15 or higher and as a bonus i happen to roll 1 i get to re roll the dice and try again once. what is the chance for success? should i consider ...
1
vote
0answers
36 views

A problem on super/sub martingale

Let $(X_n, \mathscr{F_n}), n \geq 0$ be a super martingale and $T$ an $\{F_n\}$-stopping time a.s. bounded by $N \lt \infty$. Show that $$ E[|X_T|] \leq 3 \max_{n \leq N} E[|X_n|]$$ I can prove that ...
0
votes
1answer
17 views

X/Y probability being within a range

X and Y are two independent variables with a uniform distribution from 0 to 1. What's the probability of 1 <= X/Y <=2? Is it 1/4?
1
vote
2answers
65 views

uniform distribution over disk

Given two independent random variables $A$ uniform on $[0,1]$ and $B$ uniform on $[0,2\pi]$. Obtain the joint pdf, tranform to the disk, if necessary modify to obtain the uniform pdf over the disk. ...
0
votes
1answer
25 views

Quicksort probabilistic analysis

Let us say that we randomly pick up a pivot element and partition the array around it. What is the probability that we always pick the pivots in subsequent recursive calls such that it partitions the ...
1
vote
0answers
16 views

Calculating the left pseudoinverse of a Matrix whose columns are Probablity Mass Functions

I have a matrix $A_{m\times n}$, where $A_j$ , a column of $A$ represents a probability mass function, and so the sum over the column is 1. This is true for all the columns of A, i.e. $\forall j \in ...
1
vote
2answers
14 views

PMF of X: Number of trials to draw a chip

Let a bowl contain 10 chips of the same size and shape. One and only one of these chips is red. Continue to draw chips from the bowl, one at a time and at random and without replacement, until the red ...
2
votes
1answer
52 views

A probability problem I am stuck on

A cell contains $N$ chromosomes, between any two of which an interchange of parts may occur. If $r$ interchanges occur then what is the probability that exactly $m$ chromosomes were involved? The ...
0
votes
1answer
38 views

Gamma and a poisson distribution

All I know is that $P(X=x)=e^{-5x}\frac{5^x}{x!}$ where $x\geq 0$. The formula that im using is $E(Y)=\int E(Y|X=x)f_x(x) dx $ where $f_x(s)\int f(x,y) dy $=. Also I guess that from the hint that ...
-2
votes
0answers
14 views

probability ad mutual info [on hold]

S is a random variable takes values 0 or 1 with p=1/2 and 1/2. X = a random variable that is Poisson with rate wS (w is a constant). Z is an rv that is poisson with rate lambda. Y=X+Z. What is ...
0
votes
0answers
30 views

A coin is flipped n times and let be the number of heads [on hold]

A die is rolled, and then flip a fair coin as many times as the die shows, What´s the expected number of heads?. There were three heads, what´s the expected number that was rolled on the die?
1
vote
1answer
27 views

Proof of addition rule of probabilities with 4 events

I need to show that, given a event space and four events. If the only non-empty intersections between them are $A\cap B$, $B\cap C$, $C\cap D$, $D\cap A$, then: $P(A\cup B\cup C\cup ...
0
votes
2answers
36 views

PMF of number of heads of 4 coin tosses

Let X equal the number of heads in four independent flips of a coin. Using certain assumptions, determine the pmf of X and compute the probability that X is equal to an odd number. I initially ...
1
vote
1answer
28 views

Derive the marginal probability function for X

Question: Suppose $X$ and $Y$ are discrete random variables with the following joint distribution: $P_{XY}(X=x_i, Y=y_j)=\dfrac{1}{n^2}, \,\,\,\, x=1, 2, ...., n \,\,\,\, y=1,2,...n$ Derive the ...
1
vote
0answers
36 views

Expectation of $\frac{1}{X+1}$ for a geometric random variable

I am confused over $E(\frac{1}{1+X})$ where $X$ is geometric distribution with parameter $p$. The book wants me to prove that $E(\frac{1}{1+X})=log((1-p)^{\frac{p}{p-1}})$ Here's what I did. ...
1
vote
0answers
23 views

Locate proof of Second Fundamental Theorem of Asset Pricing

Where can I find a $\textbf{rigorous}$ proof of the Second Fundamental Theorem of Asset Pricing. That is, A market is complete if and only if it has a unique risk neutral measure. Please do not ...
2
votes
2answers
28 views

Card with 2 numbers, and extraction of 5 numbers from a box with 50 different numbers from 1 to 50.

In a game, five numbers between 1 and 50 are extracted from a box. I have a card on which are written two numbers between 1 and 50. Calculate the probability that both numbers will be drawn from the ...
1
vote
1answer
20 views

3 selected cards on a set of 7 cards from a deck of 40 different cards.

What is the probability that, pulling out 7 cards from a deck of $40$ different cards, without reinserting the cards in the deck, there are $3$ cards that I wrote on a piece of paper in advance (that ...
0
votes
1answer
23 views

What is the probability of drawing of exactly one king if you draw two cards without replacement from a deck of cards? [on hold]

What is the probability of drawing of exactly one king if you draw two cards without replacement from a deck of cards?
0
votes
2answers
26 views

If $P(X \geq k) = p^k$, for $k=0, 1, 2,…$ then $P(X=k)=p^k(1-p)$

If $P(X \geq k) = p^k$, for $k=0, 1, 2,...$ then $P(X=k)=p^k(1-p)$ The converse is immediate but I don't know how to approach the direct implication.
0
votes
1answer
22 views

Conditional Probability about filling gas tanks [on hold]

At a certain gas station: 40% of the customers use regular gas $(A_{1})$ 35% of the customers use plus gas $(A_{2})$ 25% of the customers use premium gas $(A_{3})$ Of those customers using ...
0
votes
0answers
11 views

Presenting a multinomial dstribution as some function of underlying binomials

I have a multinomial distribution, which arises, let's say, for the sake of clarity, from $N$ rolls of unfair $S$ sided dice and labels on the sides are non-integer. I know the probability for each ...
0
votes
0answers
24 views

Fermat number factor probability

I found a question I couldn't solve: What is the probability that $2^{2^{12}}+1$ has a prime factor of $70$ digits? I found this problem hard as many number has more small prime factors than large ...
1
vote
3answers
30 views

Poker game full house

I'm dealing with an exercise which deals with the poker game. I need to calculate the probability of getting a full house. Full house is getting 3 cards of the same type and 2 cards of the same ...
1
vote
2answers
31 views

Let U and V be independent continuous random variables, identically distributed uniformly over [0,1]

Let $U$ and $V$ be independent continuous random variables, identically distributed uniformly over $[0,1]$. Show that for $0 \leq x\leq1$ , $$P(x < V < U^2)= \frac{1}{3} - x + \frac{2}{3} ...
1
vote
1answer
23 views

Finding an isotropic joint density from a marginal

I'm trying to find out weither it is possible or not to recover an isotropic bivariate pdf from one of its marginal pdf. By isotropic, I mean that the density only depends on the radius when ...
0
votes
1answer
31 views

Beginner Econometrics question about probabilities for a normal variable

$Y \sim N(\mu, \sigma^2)\implies (Y-\mu)/\sigma$ Prove that this has a Mean of $0$ and a Variance of $1$.
1
vote
0answers
13 views

Probability density function of sum of random variables [duplicate]

Assume $X_i$ probability density function is : $$f(x,\lambda)=\Bbb{I}_{(0,\infty)}(x)\lambda \exp(-\lambda x)$$ how to find the probability density function of $\sum X_i$ ? The result is ...
1
vote
1answer
24 views

Probability of “either/or” and “neither” for two independent events

This is a problem from GRE quantitative section practice book. The probability of rain in Greg's town on Tuesday is $0.3$. The probability that Greg's teacher will give him a pop quiz on Tuesday is ...
0
votes
1answer
18 views

Transformation of Random Variable results in strange CDF

I'm trying to transform a RV according to $Y=X^{-a}$ with $a>0$ and X being uniformly distributed in $[0,A]$: $ F_X(x) = \begin{cases}0 & x<0 \\ x/A & 0\leq x \leq A \\ 1 ...
1
vote
2answers
40 views

Please help me simplify this complicated probability equation

The equation is: $A_n = \text{probability that the n-th unit in a circuit works} = (1-p)$. $$P(\text{system works}) = P[(A_1 \wedge A_2) \vee A_3 \vee (A_4 \wedge A_5)]$$ I've verified that this is ...
0
votes
3answers
40 views
+50

Finding marginal density from a joint density when range of random variables are dependent on one another.

I have two joint density problems, where I would like to find the marginal density. The first one: $f(x,y) = 24xy, 0 \leq x \leq 1, 0 \leq y \leq 1, 0 \leq x+y \leq 1$ So, I "integrate out y" and ...
0
votes
1answer
22 views

Probability of multiple chances with at least one result

There are some similar questions but I can't solve this to my reality. In a lottery, say that are 10000 balls, and only 36 are the ones that I want. Ok so for 1 ball randomly selected, I will get a ...
1
vote
4answers
27 views

Probability of alternating alternating positions

I was given the following questions: I am stuck on question b. The probability is defined as $P(E) = \frac{n(E)}{n(S)}$ I believe $n(s) = 11!$ (or is it $\frac{11!}{(6!5!)}$) I am stuck on ...
0
votes
0answers
15 views

counting occurence of subgraphs by counting their occurence in larger subgraphs

I have a mental block in fully understanding the following notion. Let $G$ be a graph of order $n$ and $H$ a fixed small graph of order $k \le n$. Suppose that there are $d$ copies of $H$ as an ...
0
votes
0answers
11 views

Maximizing utility function equivalence

Let's denote our expected utility $U_{\pi} = \int ((1-e^{-kx}) \frac{1}{\sqrt{2\pi}\sigma}e^{-(x-z)^2/2\sigma^2} dx$ I'd like to show that maximizing this is equivalent to maximizing $E[X] - ...
1
vote
1answer
62 views

Probability of a substring occurring in a string

Consider a random string of length $n<\infty$ where each digit can be between 0-9 with equal probability and a substring of length $k<n$ consisting of only zeros. What is the probability of ...