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

The probability of drawing at least two diamonds among three cards drawn at random with replacement

I am learning Random variables and Probability distribution. I got this question some what hard! Can somebody help me solve this please. Three cards are drawn at random successively with ...
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0answers
18 views

Probability of two people calling the same person at the same time [on hold]

I have a smartphone, and a few days ago, I somehow called someone in my contacts while my smarthpone was in my back pocket while standing up, at the same time a person I was talking to called them. ...
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0answers
18 views

Mean absorption time for pure birth process

Let $\xi_t$, $t\geq0$, be a pure birth process, with $P\{\xi_{t+h} = i +1 | \xi_t = i\} = \lambda^ih + o(\lambda)$, as $h \downarrow 0$. At $t=0$, $\xi_0 =1$. Let $\tau = \min\{t ~|~ \xi_t = N\}$. ...
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1answer
16 views

Expected value of $(\overline{X} - 5)^2$?

$X_1, \ldots, X_9$ are 9 random samples from a N(5, 9). I am looking for the distribution ofExpected value of $(\overline{X} - 5)^2$. $$E[(\overline{X} - 5)^2] = E[\overline{X}^2 - 10\overline{X} + ...
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0answers
8 views

Testing hypothesis about window non-overlap

I have a large number (~1.5 million) of protein sequences, each of them of different lengths.There are 6 schematic examples in the attached image. Within each of these sequences, there are >= 0 ...
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0answers
10 views

How do I combine probability estimates of two equivalent/mutually inclusive events?

Let's say I'm pregnant with fraternal twins. One of them hangs out in the left side of my womb, and the other hangs out on the right (I have no idea how biology works). We've applied a flaky test to ...
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0answers
11 views

Proving that a process has the Markov property

Let $X_t=xe^{ct+aB_t}$ where $B_t$ is one dimensional Brownian motion. How would I prove this is a Markov process using the expectation definition of a Markov process, i.e., ...
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2answers
57 views

Why is this expectation true?

Working with Rao-Blackwell, this came up: $$E[2X_1 \mid \max(X_i) = t] = 2\left(\frac{1}{n}t + \frac{n-1}{n}\frac t 2\right)$$ Where X are uniform(0, $\theta$). What are the intermediate steps? I'm ...
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0answers
31 views

Probability of drawing a run of a specific color from an urn with two colors of balls

I was sent a puzzle involving an urn with 128 white balls and 288 black. If the balls are drawn without replacement until the urn is exhausted, what is the probability that a sequence of 10 or more ...
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0answers
14 views

Expected number of dice rolls to uniquely determine values of the faces

Suppose we have $k$ fair $n$-sided die (so each face rolls with probability $1/n$), with each face of the die labelled as $a_i$ $ (i=1, \ldots, n)$, with the values of the $a_i$ being unknown to us. ...
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2answers
35 views

Probability of Dialing Correct Digits

Jason remembers only the first five digits of a seven-digit phone number, but he is sure that neither of the last two digits is zero. If he dials the first five digits, and then dials two more digits, ...
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0answers
28 views

What does the notation $\textbf{x} \langle\textbf{Y} \rangle $ mean if $\textbf{Y} \subseteq \textbf{X}$ for random variables?

I was reading daphne's Probabilistic Graphical Models book and she introduces some notation about sets of random variables that I am confused about (on page 21 section 2.1.3.2). Before I ask my ...
2
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1answer
34 views

Finding conditional distribution

Let $X$ and $Y$ be independent $Exp(1)$-distributed random variables. Find the conditional distribution of $X$ given that $X + Y = c$ ($c$ is a positive constant). this is my idea: $$f_{X \mid ...
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0answers
29 views

Laplace transform of product of two function

Consider the following integral of product of two function $$ \int_0 ^t f(s)g(s-t)ds $$ i want to know the laplace transform of above term w.r.t t. if $g(s-t)$ is replaced by $g(t-s)$, there is a ...
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0answers
28 views

Can we have Tchebysheff's equality?

Assuming $μ=0$ and $σ=1$, and also that $X$ is symmetric about $μ=0$, Is there a discrete random variable $X$, satisfying the assumptions above, which takes on (not necessarily positive) integer ...
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2answers
27 views

How to draw a continuous distribution function [on hold]

for drawing any function,we must just input all values on its domain to calculate its f(x) values and then draw it.How should one draw a continuous probability distribution function,while we know that ...
4
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2answers
58 views

Probability for Magic Trick

I had a probability problem to solve , but could not proceed further , we have a m identical decks having n cards , where each deck has n different cards . Now shuffle them and select n cards . Now a ...
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1answer
18 views

Probability regarding success and failure…

I have a question.... A man can hit a target once in $4$ shots, if he fires $4$ shots in succession, what is the probability that he will hit his target? I did this, probability of hit = ...
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1answer
59 views

Expected number of coin tosses until a run of $k$ successive heads occurs

Suppose each coin toss is independent, what is the expected number of coin tosses until a run of "k" successive heads occur? Tried finding a recursive expression to solve the problem but got ...
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3answers
101 views

Birthday “Paradox” - another, different, version!

Background Many people are familiar with the so-called Birthday "Paradox" that, in a room of $23$ people, there is a better than $50/50$ chance that two of them will share the same birthday. In its ...
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0answers
14 views

the intuitive difference between expected utility and utility of expected profit in a gambling game

What is the intuitive difference between expected utility and utility of expected profit in a gambling game ? Which one is the "usefulness of the game" to a player ?
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2answers
17 views

Math, Probability on replacement and with out replacement!!

I am weak in probability, I am confused with replacement and without replacement, can someone please explain the problem.. A bag contains 3 blue and 2 red marbles, two marbles are selected at ...
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2answers
41 views

A student appeared at 3 examinations…

I am very weak in probability, I have a question.... A student appears at $3$ examinations. The probability of passing each exam is $\frac15,\, \frac16,\, \frac17\,$ respectively. Then what is the ...
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0answers
16 views

Expected value of adjacent bulbs go off [on hold]

Given $n$ light bulbs with exponential distribution for the probability when the bulb will be turned off, what is the expected time that any two adjacent bulb will be off?
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0answers
24 views

Distribution of an upper limit of a sum of random variables

Let $\{X_{n,j},n\geqslant1,j\geqslant1\}$ be independent and identically distributed random variables. Denote $S_{n,k}=\sum_{j=1}^kX_{n,j}$. Let $\{Z_n,n\geqslant1\}$ be a sequence of random variables ...
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1answer
30 views

Help proving $Pr(\mathcal{X})= \phi_1(X,Z)\phi_2(Y,Z)$ if $ P \models (X \perp Y | Z)$ and $\mathcal{X}=X \cup Y \cup Z$

I was trying to prove the following: if $X,Y,Z$ were three disjoint subsets of variables such that $\mathcal{X}=X \cup Y \cup Z$, Prove that $ P \models (X \perp Y \mid Z)$ if and only if we can ...
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2answers
19 views

Laplace transform of noncentral chi-square distribution

I'm interested in non central chi-square distribution. More specifically, i want to derive the laplace transform of noncentral chi-sqruae disribution or density function. Let me know whether it ...
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1answer
32 views

Conditional probability and a game of tennis

In a best of 5 tennis match, Alex and Bob are equally likely to be the better players. If Alex (Bob) is the better player, he wins a set with probability 0.75 (0.75) independently of the outcome of ...
1
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1answer
41 views

Unfair election results probability

Folks, last time I've manipulated probabilities was some $30$ years ago so I'm struggling with the following problem: Suppose we have $N=6000$ candidates for $M=100$ seats in a parliament. Each ...
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1answer
34 views

Expected number of bins with more than one ball

Suppose that $n$ balls are randomly thrown into $N$ bins. We can compute the expected number of bins that contain at least one ball as $E(X) = N(1 - (1 - 1/N)^n)$. Now, suppose that instead we are ...
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4answers
208 views

Calculating probabilities in horse racing!

I've seen a few similar threads to this on different forums but they don't seem to conclude to a satisfactory answer. My question is this: If you have 3 horses, A, B, and C and you know the winning ...
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2answers
34 views

If $X$ has CDF $F$, how can I find the CDF of $U= \max \{0,X \}$?

If $X$ has CDF $F$, how can I find the CDF of $U=\max\{0,X\}$? Obviously the suport of $U$ consists solely of nonnegative values. Am I right then in thinking that for $u=0, F_U (u)=F_X(0)$ and for ...
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1answer
37 views

Is there a set of 69 length-6-sets out of 46 numbers [1..46] so that those length-6-sets “cover” all possible 1035 length-2-sets of 46 numbers?

1.) For this question, we have 46 numbers (balls, cards, whatever): {1,2,3,4 .... 45,46} ======================= 2.) Each length-6-set of 46 numbers ( e.g. {1,2,3,4,5,6} or {1,13,16,17,32,46 } ...
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0answers
24 views

Probability of a 21 deck with jokers [on hold]

There 21 cards in a deck. There are 5 pairs, a king, a 10, a 7, a 5 and joker. What's a probability of getting any pair from the deck? Do not include the pair of jokers to the number of cards in the ...
1
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1answer
41 views

Sum of dependent normal random variables

Let ${\bf X} =(X_1,\ldots,X_n)'$ be a vector of random variables that may be dependent and let ${\bf a}=(a_1,\ldots,a_n)'$ and ${\bf b}=(b_1,\ldots,b_n)'$ be nonrandom vectors with $a_i \neq 0$ and ...
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0answers
22 views

Show that $ \prod_{k=1}^n [1 + p_{nk}(e^{it} - 1)] \rightarrow e^{\lambda(e^{it} - 1)}, n \rightarrow \infty $

Suppose that $0\leq p_{nk} \leq 1, 1 \leq k \leq n$, $\max_{1 \leq k \leq n} p_{nk} \rightarrow 0, n \rightarrow \infty$ and $\sum_{k=1}^n p_{nk} \rightarrow \lambda$. Show that $$ \prod_{k=1}^n ...
3
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1answer
22 views

Distribution of random variable

I need help with this problem: Let $(X_n)_{n\in \mathbb{N}}$ a sequence of i.i.d$\sim $Uniform$(\{0,\dots,9\})$ random variables. What is the distribution of $$X= \sum_{n=1}^{\infty} X_n 10^{-n}$$ ...
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0answers
8 views

Generate quadrature points from a distribution

Is there any method to generate quadrature points from any arbitrary probability distribution, $p_{X}\left(x\right)$? We already know about Gauss Hermite rule for Normal distribution, Gauss-Laguerre ...
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1answer
62 views

Combination Problem with Sofa [on hold]

Suppose we have 5 sofa on room A. in this room, 4 students seated on these sofa. These Strudents go to another room for eating dinner, and after that come back to room A. how many way the students can ...
1
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1answer
20 views

Density of a sum

Let $X, Y$ be random variables having the joint density $f(x,y) = (a+1)(a+2)(y-x)^a, 0 \leq x < y \leq 1$, and $f(x,y) = 0$ elsewhere. Compute the density of $Z = X+Y$. My solution doesn't match ...
2
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1answer
46 views

Sufficient statistic

Let $\mathbf{X}=(X_1,\ldots,X_n)$ with joint frequency function $f(\mathbf{x};\theta_1,\theta_2)$ where $\theta_1,\theta_2$ vary independently. The set ...
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1answer
20 views

How to compute the difference between two numbers using a weighted formula?

Currently at work we use the formula ((expected-actual)/expected)*100 to show the difference between two numbers, however, this formula shows extreme differences for small numbers. For example, in the ...
1
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1answer
34 views

Strange proposition in probability book for conditional probability

I found the following proposition (15.1) in the probability book of Heinz Bauer: Let us given that $X$ is a numeric random variable on $(\Omega,\mathcal{A},P)$ which is non-negative / ...
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0answers
40 views

the usage of the PDF

We know that in a continuous distribution,the probability in a specific point like x is zero.If it is this way, then what does exactly the probability function-f(x)- of a distribution like normal ...
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1answer
30 views

Find joint distribution of distance to origin from points chosen uniformely inside spheres

I have the following problem. A point $P $ is chosen uniformely from the unit sphere $|X |\le1$, where $X \in R^3 $. Then an other point $P' $ is chosen uniformely from the spere centered at the ...
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1answer
23 views

Is it possible that a randomized recursion has a nonzero probability of either converging or diverging?

I have very little "hands-on" experience with probability, but here is my context: I was looking at the random Fibonacci sequence: $$f_0=f_1=1, f_n=f_{n-1}+Xf_{n-2}$$ where $X$ is chosen randomly ...
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1answer
61 views

Will I will be able to sit and watch the movie?

Recently I went to the theater. When I came to buy my $3$ tickets (two friends and I), the machine tells me that there is $18$ seats out of $300$ ($15$ rows of $20$ seats). What is the probability ...
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6 views

How to find confidence interval of quotient

This site does a good job of explaining how to find a confidence interval for reliability $R(t)$. It also explains how to find conditional reliability $R(t|T) = R(t + T) / R(T)$. However, it does ...
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2answers
63 views

In 30 boxes are 15 balls. Chance all balls in 10 or less boxes?

Question1: I found 30 boxes. In 10 boxes i found 15 balls. In 20 boxes i found 0 balls. Afer i collected all 15 balls i put them randomly inside the boxes. How much is the chance that all balls are ...
2
votes
1answer
21 views

What are the probability that the first two rows of the class are full?

I was boring in my class. So I ask myself the question: What are the probability that the first two rows of the class are full? Knowing that we're $25$ students in my class and the class have ...