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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2
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0answers
5 views

Largest jumps of a spectrally positive $\alpha$-stable process

Let $X(.)$ be a (strictly) $\alpha$-stable process (with $\alpha \in (1,2)$). Assume also that $X(.)$ is spectrally positive (its Lévy measure is concentrated in $[0,+\infty)$). I am looking for a ...
0
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0answers
4 views

different combinations of numbers

Can anyone help me pick 1,000 combinations of six numbers from two separate pools of numbers - five different numbers from 1 to 75 and one number from 1 to 15?
-3
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1answer
18 views

what is the expected number of times a 6 will be rolled? If a 6 is rolled 10 times what can be said about the die? [on hold]

A die is rolled 20 times what is the expected number of times a 6 will be rolled? If a 6 is rolled 10 times what can be said about the die?
0
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0answers
4 views

Hitting times of a biased continuous time random walk

Let $X_{s \geq 0}$ be a continuous time random walk on $\mathbb{Z}$, i.e. waiting times between jumps are exponentially distributed with mean one. The random walk is biased: $\mathbb{P}(X_s\text{ ...
0
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0answers
4 views

Finding upper critical value with chebyshev's inequality

Consider $X$ is a Poisson random variable with distribution $X$~$Pois(\theta)$. I define the mean in my hypothesis as $\lambda$ and nominal significance level $\alpha$. Null hypothesis $H_0 : ...
-1
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1answer
40 views

Cards probability problem

Two players; the dealer and a player. The player is given three cards face down. The dealer turns over a 2 (let's say of hearts). Before the player turns any cards over, what is the probability that ...
2
votes
1answer
22 views

Symmetric function of two normal distribution implies bilinear

This question is related to my previous question which was partially answered my @MichaelHardy. Let $X$ and $Y$ be two independent standard normal random variables. Now, suppose that ...
0
votes
1answer
15 views

Question involving the PDF of a function of a random variable.

I'm trying to understand the setup for problem 3.1, from M.G. Bulmer's Principles of Statistics (Dover, 1967). Suppose that $X$ is a continuous random variable, and that $Y$ is a linear function ...
-1
votes
1answer
37 views

Exponential distribution and expectation [on hold]

Given that $X ∼ Exp(λ)$, compute $\mathbb{E}[e^{−(X−\lambda/2)^2} ]$. Your answer should not be left as an integral. so you would get $\mathbb{E}[e^{-x^2+x\lambda-\lambda^2/4} ]$? Can this question ...
0
votes
3answers
47 views

Probability on selecting balls

If I have B black balls and W white balls in a bag, what is the probability that the last one I select is white? How shall I solve this problem? I am not sure how to make a start, is it correct ...
1
vote
1answer
21 views

How to approximate the expected value in this problem

I was solving this probability problem and I don't know how to approximate the expected value. Thanks in advance! Problem definition: The durability of a tire in a city of South Africa is a ...
1
vote
1answer
36 views

Probability and Name of Distribution

Suppose $X$ has PDF $f_X$ given by \begin{align*} f_X (x) = \begin{cases} \frac{\alpha x_0^\alpha} {x^{\alpha+1}} &\text{if $x ≥ x_0$,}\\ 0 &\text{if $x < x_0$,}\end{cases} \end{align*} ...
1
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0answers
17 views

Transition density of an AR(1) process?

If we have an AR(1) process, i.e: $X_{t+1} = \alpha X_t + e_{t+1}$ with $X_0=0$ then what is its Markov Chain transition density? We know that for a Markov chain, the following holds: $P(X_{t+1}\leq ...
0
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0answers
29 views

2 people being born and dying on same dates with same names [on hold]

With 100 first names and 500 last names to choose from, odds of 2 people with same first and last names having exact dates of birth and death including year out of 100 million people? (this is a ...
0
votes
0answers
42 views

Write a random variable as a convex combination of other 2

I'm trying to prove that if $f:[0,1]\to\mathbb{R} $ is continuous and convex, then the Bernstein polynomials are too. The hint that I've got is this: "Let $p_1 < p_2 < p_3<1$ and consider ...
1
vote
1answer
23 views

Determine $P(S_n\leq1)$ where $S_n=\sum_{k=1}^nX_k$

Suppose that $X_n$ are i.i.d. $Uniform(0,1)$ random variables. Let $S_n=\sum_{k=1}^nX_k$ with $S_0:=0$. Then, determine $P(S_n\leq1)$. I know that maybe by using Characteristic function of $S_n$ ...
0
votes
1answer
32 views

Problem of Conditional Probability

I am learning Probability from Sheldon Ross book. One of the problems starts by giving the probability $P_N$ that there are no matches when $N$ people select from among their own $N$ hats as ...
1
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1answer
19 views

Expected value using indicator variables

Randomly, $k$ distinguishable balls are placed into $n$ distinguishable boxes, with all possibilities equally likely. Find the expected number of empty boxes. PROPOSED SOLUTION: Let $I_j$ be the ...
2
votes
1answer
29 views

Sufficient condition for $E(wu\mid v)=0$ given that $E(u\mid v)=0$?

I'm trying to figure out what condition concerning $w$ and $v$ would be enough for me to infer that $E(wu\mid v)=0$ given that I already know $E(u\mid v)=0$. Clearly, $w$ is a constant works: ...
-2
votes
2answers
60 views

I'm not able to solve conditional probability questions!! [on hold]

You are given: $\Pr(A) = {2\over 5}$, $\Pr(A ∪ B) = {3\over 5}$, $\Pr(B\mid A) = {1\over 4}$, $\Pr(C\mid B) = {1\over 3}$, and $\Pr(C\mid A ∩ B) = {1\over 2}$. Find $\Pr(A\mid B ∩ C)$ Okay, ...
-1
votes
1answer
32 views

Conditional Gambler ruin problem

A gambler repeatedly plays a game where in each round, he wins a dollar with probability 1/3 and loses a dollar with probability 2/3. His strategy is “quit when he is ahead by 2 dollars”, though some ...
0
votes
1answer
13 views

Inverse function for a sort of negative binomial distribution

I am trying to find the inverse function of $f(p) = \sum_{k=0}^{6}{\binom{6-H+k}{k} p^{7-H} (1-p)^k}$, where $0 \leq H \leq 6$ is a constant integer. Any ideas on how to do this? Or perhaps equally ...
0
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0answers
21 views

Quadrant probability of non-centric bivariate normal distribution

Suppose $(X,Y)$ has a bivariate normal distribuion with non-zero mean vector $\mu$ and covariance matrix $\Sigma$. What should $\mathbb{P}(X>0,Y>0)$ be? My attempt gives me an definite ...
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3answers
56 views

Gender Birth problem - Conditional probability

A family has two children. Assume that birth month is independent of gender, with boys and girls equally likely and all months equally likely, and assume that the elder child’s characteristics ...
0
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2answers
53 views

How many divisors of the combination of numbers?

Find the number of positive integers that are divisors of at least one of $A=10^{10}, B=15^7, C=18^{11}$ Instead of the PIE formula, I would like to use intuition. $10^{10}$ has $121$ divisors, ...
1
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0answers
44 views

Lottery Expected Value Question

Background: The Daily 3 game is a daily game, drawn every day except for Saturday and Sunday. It consists of three sets of balls, each numbered from $0$ through $8$ ($9$ is omitted due to its visual ...
3
votes
4answers
54 views

Is conditional probability always meaningful

Problem: A bag contains $4$ red and $5$ white balls. Balls are drawn from the bag without replacement. Let $A$ be the event that first ball drawn is white and let $B$ denote the event that the ...
1
vote
1answer
20 views

How to calculate the partition function of a given distribution?

As noted in A FULL BAYESIAN APPROACH FOR INVERSE PROBLEMS, let $ y = Ax + n$, where $x$ is a $m$ dimensional signal and $n$ is white Gaussian noise with precision $\beta$, so we have: $$ y|x, \beta ...
1
vote
1answer
35 views

Probability of Two People Choosing the Same Number between 1 and 50 or choosing 2 numbers that add to 50 [on hold]

If two people are asked to each choose a number between 1 and 50, what is the probability that they choose the same number, or choose numbers that add to equal 50?
1
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1answer
26 views

Counter example: $X$ and $Y$ normal imply $(X,Y)$ bivariate normal

I vaguely remember this construction from one of my courses: Suppose that $X\sim N(0,1)$ and $Z$ is $\pm 1$ with probability $\frac{1}{2}$ each. If $X$ and $Z$ are independent, then $Y\equiv XZ$ is ...
1
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2answers
19 views

Biased and fair coin in Hat flipped

Two coins are in a hat. The coins look alike, but one coin is fair (with probability 1/2 of Heads), while the other coin is biased, with probability 1/4 of Heads. One of the coins is randomly pulled ...
1
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1answer
58 views

Expected Value of a Mosquito

A mosquito is walking at random on the nonnegative number line. She starts at $1$. When she is at $0$, she always takes a step $1$ unit to the right, but, from any positive position on the line, she ...
3
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0answers
33 views

What is the area covered by a Random walk in a 2D grid?

I am a biologist and applying for a job, for which I need to solve this question. It is an open book test, where the internet and any other resources are fair game. Here's the question - I'm stuck on ...
1
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1answer
42 views

Probability of getting a five digit number divisible by 5 but with no two consecutive digits identical

A five digit number is written down at random. What is the probability of getting a number that is both divisible by 5 and doesn't have any 2 consecutive digits identical? I tried to analyse the ...
0
votes
1answer
37 views

An urn full of balls problem [on hold]

Among $10$ balls in a bag , $6$ of which are black , $4$ white , $3$ balls were removed randomly . What is the probability that from the remaining $7$ balls , if one ball is chosen at random , it is ...
-2
votes
1answer
26 views

a pin is spun on a flat table [on hold]

A pin whose centre is fixed on a flat table is randomly and independently spun twice.Each time the final position is noted by drawing a line segment.what is the probability that the smallest angle ...
1
vote
1answer
32 views

If 3 people put their hat in a box, but the hats are mixed up. How likely is it that AT LEAST one person getting their hat back.

If 3 people put their hat in a box, but the hats are mixed up. How likely is it that AT LEAST one person gets their hat back. Consider all possibilities. Then what about 4 people. Please use ...
0
votes
3answers
28 views

Probability rolling two different sided die and sum being a number

I'm building an app (for those curious, for DnD) and I came across an issue with some math I did. I need to know the probability of rolling a certain number when there are two or more different sided ...
-1
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0answers
32 views

boxes around a circle [on hold]

Suppose You have $10$ boxes numbered from $1,2,3,......,10$ arranged sequentially around a circle. We perform $100$ trials.At each step you have to choose a specific box with probability $\frac ...
-1
votes
1answer
58 views

How and why do rumors/gossip spread? [on hold]

I should clarify what I mean by gossip (this is taken from wiki): Idle talk or rumor, especially about the personal or private affairs of others. That seems accurate enough, though alternative ...
1
vote
0answers
24 views

Regression in Bivariate Normal

Suppose $(X_i \hspace{4pt} Y_i)'$ are $i.i.d$ $N_2 (\bf{\mu,\Sigma})$, $i=1(1)n$ where $E(X)=\mu_x$, $E(Y)=\mu_y$ and $\Sigma$ is given by \begin{bmatrix} \sigma^2_x & \rho\sigma_x\sigma_y\\ ...
0
votes
0answers
15 views

Find conditional probability of a mixture model

given is the following: A mixture model comprises a non-observable $\{ 0,1\}$-valued random variable $X$ such that $P(X=1)=1-P(X=0)=\pi$ and an observable variable $Y$ such that $Y\mid X=0$ is ...
2
votes
1answer
23 views

Probability a card can win a trick with a trump suit

I'm working on the AI for a card game that uses a standard deck of 52 cards consisting of 13 cards in 4 (spades, clubs, diamonds, hearts) suits. Each player starts with 13 cards in their hand. ...
4
votes
4answers
129 views

What is the probability of getting a 3 or higher on a six sided die, if I reroll after failing the first time?

Just as the question says... What is the probability of rolling a 3 or higher on a six sided die, if I reroll the die a second time when I fail the first time?
0
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0answers
51 views

Question about conditional probability [on hold]

I am working on some exercise questions from probability. I am stuck at this question. Can somebody help me to solve this. I would really appreciate. In a certain country, $35$ percent of people ...
0
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0answers
13 views

Picking Marbles and Estimating the Expected Cost

This is a general version of a game I play. Suppose there is a bag of marbles that consists of 4 different marbles : Silver ...
2
votes
2answers
73 views

Probability of Level Crossing

I am kind of stuck on how to proceed on this. $X_n$ is an IID process with $$f_{X_n}(y)= \frac\lambda2 e^{-\lambda |y|}$$ There is a stationary autoregressive process $Y_n$ defined as $$Y_n=\rho ...
0
votes
0answers
40 views

what is the difference between statiscal averagre and average?

I'm reading a book on synthetic aperture radar and it is said that: The term $\sigma^{\circ}$ is the averaged radar cross section per unit area, also called the scattering coefficient or ...
1
vote
2answers
68 views

Ways of coloring the $7\times1$ grid (with three colors)

Hints only please! A $7 \times 1$ board is completely covered by $m \times 1$ tiles without overlap; each tile may cover any number of consecutive squares, and each tile lies completely on the ...
0
votes
1answer
34 views

Prove that if events $A,B$ independent of C then $P(A\cap B\cap C)= P(A\cap B)P(C)$

I am trying to prove why the intersection of two events $A, B$ that are independent of C is also independent of C so that the following equality holds: $$P(A\cap B\cap C)= P(A\cap B)P(C)$$ ...