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 (2)

0
votes
0answers
14 views

Bayesian statistics and Basis for continous functions

I was thinking about Bayesian statistics, and one thought bothered me: In Bayesian statistics, we assume that the pdf $p(x)$ can be described as: $p(x)=\int f(x|\theta)g(\theta)d\theta$ usually ...
0
votes
2answers
28 views

Finding the mode of a distribution

I've been trying to get a better understanding of distributions. So far I understand how we get the formulas for mean and variance (by looking at the derivative of the moment generating function). ...
0
votes
1answer
18 views

Help needed with Probability Question

A card is drawn at random from a deck of playing cards. If it is red, the player wins 1 dollar; if it is black, the player loses 2 dollars. Find the expected value of the game.
3
votes
3answers
125 views

Probability and math

You have a drawer with $6$ loose blue socks, and $10$ loose brown socks. If you grab two socks from the drawer in the dark (random draw), what is the probability that you draw a brown pair? I have ...
0
votes
1answer
33 views

Rolling 1 die 5 times

One die is rolled five times. How many different results are possible? Of those, in how many ways can there be exactly 2 rolls of 4?
2
votes
1answer
14 views

Conditional probability with max(X, Y)

Let $Y_n=$ the outcome of the $n$-th die roll, let $X_{n+1} = \max \{X_n, Y_{n+1}\}$ with $X_1=Y_1$. What is $P(X_{n+1}=j \ | X_1=i_1, ..., X_n=i)$? I know that it is $P(\max \{X_n, Y_{n+1} \}=j \ | ...
0
votes
0answers
10 views

multivariate interval estimation

I have several samples of probabilistic vectors, i.e, each sample is of the form $(x_1, \cdots, x_n)$ such that $\sum_{i=1}^n x_i\leq 1$ (they are sub-probabilistic vectors), how can I obtain a ...
-1
votes
1answer
24 views

probability for beginners : simple question

Could you answer the following please... If we roll a die once and define Event A: The face value is even but less than 6 Event B: The face value is not 1 or 6. a) Then what is the ...
-1
votes
2answers
21 views

What is the probability of winning in a shootout? [on hold]

Person A can make $\frac{2}{5}$ of his free throws Person B can make $\frac{3}{4}$ of his free throws They take turns with person A going first The first person to make his free throw is the winner ...
0
votes
1answer
36 views

Understanding the sum of random variables

I am currently learning probability theory. I have two questions: I would like to know through an example what is meant by the sum of random variables (r.v.). To make things simple let consider only ...
1
vote
1answer
25 views

Proving a statement about probability theory

Let X be arandom variable. Consider any constant $c\gt 0$ how to prove the following satement $$\sum P(|X|\ge cn) \lt \infty \iff E(|X|)\lt \infty $$ My answer trail: $E[|X|]=\sum_X|X|P_x(X)\lt ...
1
vote
0answers
11 views

Suggestions for dealing with these order statistics

Consider a collection of $n$ random variables $X_i \sim N(\mu, \sigma^2)$, ($i = 1,2,\ldots, n$) and a random variable $X \sim \text{Exp}(\lambda)$. All $X_i$'s and $X$ are mutually independent. Let ...
1
vote
1answer
25 views

Bayes theorem - is it applicable in any case?

I'm studying the Bayes' Theorem and I have a doubt. In this wikipedia page there's an example of application for the following events: ...
0
votes
1answer
19 views

Calculating the probability of getting a full bucket in a hash table with open addressing

I have a problem where I'm trying to calculate the probability of getting a full bucket when I use a hash table with open addressing. What I have: A hash table with 128 buckets, each bucket can ...
0
votes
1answer
38 views

some properties of $\nu$ measure

For any given function $F$ satisfying the following properties $0\le F(x)\le1,\forall x\in\mathbb R$ $F(x)\le F(y),x\le y$ $\lim_{x\to-\infty}F(x)=0,\lim_{x\to\infty}F(x)=1$ $F$ is continuous from ...
0
votes
1answer
27 views

Simultaneous density function of two continuous variables, X and Y.

I'm having issues with calculating the simultaneous density function of two continuous variables, X and Y. I took a screenshot of the information: How should I start? I know that if the two ...
2
votes
1answer
14 views

How to find data distribution law using MATLAB?

Having a random variable $T \geq 0$ and a set of discrete data represented by $t=t_i$ and $P(T \leq t-i)$. My aim is to find the distribution law of $T$. Is there any fast method in Matlab that can ...
2
votes
0answers
21 views

Find the correct combination

Case 1 : if we bet on team1 with Rs.1 and win then we will get Rs.1+Rs.1 Case 2: if we bet on team2 with Rs.1 and win then we will get Rs.1+Rs.3 Case 3:if we bet on team3 with Rs.1 and win then we ...
2
votes
0answers
25 views

Hoeffding’s inequality extension

In Hoeffding’s inequality we assume that the random variables $X_i$ ,$i=1,..,n$ are i.i.d. and bounded . Is there any extension to Hoeffding’s inequality for the case that $X_i$ are identically ...
2
votes
1answer
19 views

Derive probability mass function from probability-generating function

Given the probability generating function $$G(z) = \frac{1}{2} \frac{3+z}{3-z}$$, how can one derive the pmf? I know that I have the manipulate the function into a series: $$G(z) = ...
1
vote
1answer
32 views

Understanding summations with Poisson

I'm currently doing a problem on Poisson processes and I've encountered the situation where I'm not sure why this summation is expanded as follows: And similarly I have tried expanding out the ...
0
votes
0answers
23 views

calculate a probability using the central limit theorem

$X$ is a variable of a Bernoulli distribution $ X \sim b(p)$ where $p\in(0,1)$. We also have the sequence of independent and identically distributed variables $Y_n$ with uniform distribution. $ ...
1
vote
1answer
29 views

Steve Nash’s expected value from his one-and-one free throw situation is 1.72 points. What is his free-throw percentage?

The one-on-one free throw situation works like this - for the first throw, if you make it, you get to do it again. If you miss, you don't get another chance. If you make it the second time, you get ...
1
vote
2answers
34 views

Why $p\{N>n\}=p\{X_1+…+X_n\leq x\}$.

Let $(X_k)$ a sequence iid of random variable uniform on $[0,1]$. Let $x\in]0,1[$ and $N=\min\{n\geq 1\mid X_1+...+X_n>x\}$. Why $$p\{N>n\}=p\{X_1+...+X_n\leq x\} \ \ ?$$
0
votes
2answers
34 views

Let X have density 2t on 0 < t < 1 and Y be uniform on the interval (0, 10) and independent of X. Find the density of Y/X. [on hold]

Let X have density 2t on 0 < t < 1 and Y be uniform on the interval (0, 10) and independent of X. Find the density of Y/X. Find E(Y/X) I have no ideas how to solve it now i ...
2
votes
1answer
48 views

Coin tossing: Streak count

I have a special request with regards to probability. Let's say I toss a coin 400 times. What I need to know is the average number of streaks of various lengths within such a sample. How many ...
1
vote
0answers
12 views

bias reduction when the bias depends on the true parameter

Let's say we estimate a parameter, $\theta$, by $\hat{\theta}$. For this estimator we have the following property that $$\hat{\theta}\to_{p}\theta+f(\theta)$$ where $\to_{p}$ denotes convergence in ...
-4
votes
1answer
30 views

probability question of balls [on hold]

what is the chance of getting at least one defective item if 3 items are drawn randomly from a lot containing 6 items of which 2 are defective?
2
votes
0answers
25 views

normal squared characteristic function derivation

I'm trying to derive the normal squared characteristic function, there's already a question on this but the answer has a part which is "proved as an excercise" which I try to do here. Is my proof ...
4
votes
3answers
241 views

What is the probability that 5 randomly chosen cards in a deck add up to 40 or greater?

I have made a probability game, where you have to pull out any 5 cards without looking (from a deck of 52 cards), and if all five cards add up to 40 or more, they player pulling the 5 cards from the ...
0
votes
0answers
27 views

Sum of two independent Continuous-Time Markov Chains [on hold]

This is the first time I have come across a question involving the sum of two independent continuous time Markov Chains.I know you can find the sum of two random variables Z = X + Y by finding the ...
-1
votes
0answers
17 views

If two sequence of random variables $X_n$ and $Y_n$ converge in Probability to X and Y, then X = Y a.s

If two sequence of random variables $X_n$ and $Y_n$ converge in Probability to $X$ and $Y$, then $X = Y$ a.s. Idea: I want that $P(|X-Y|> \epsilon) = 0$, for every $\epsilon >0$. We can ...
6
votes
2answers
128 views

Rolling two dice, what is the probability that two consecutive $7$s happens earlier than a $12$?

Alice and Bob are playing a game involving two dice. If a sum of 12 appears, Alice wins and they stop playing. If a 7 appears twice in a row, Bob wins and they stop playing. What is the probability ...
-1
votes
1answer
20 views

In how many different ways can a person vote based on the problem below? [on hold]

There are 9 people on the ballot for regional judges. Voters can vote for any 4. Voters can choose to vote for 0, 1, 2, 3, or 4 judges. In how many different ways can a person vote?
3
votes
0answers
29 views

Why is this class closed under difference?

We have two independent random variables $X\perp Y$ involving three spaces: $(\Omega,\mathcal{A},P), (E,\mathcal{E}), (F,\mathcal{F}).$: $$X:\Omega \rightarrow E,\ Y:\Omega\rightarrow F$$ My book says ...
0
votes
0answers
43 views

How to compute P(|X - E_Y[h(y)]| < c)?

Consider the discrete random variable $Y$, the continuous random variable $X$, and a constant $c$. The goal is to find $$P(|X - E_Y[h(y)]| < c),$$ when we are only given $P(y)$, function $h(y)$, ...
0
votes
3answers
23 views

Events with States

Bob and I are playing a game with an unfair coin that is rigged to come up heads with probability $\frac35$ and tails with probability $\frac25$. Bob goes first, we take turns, and the first player ...
1
vote
0answers
28 views

vase with blue and red balls

At first I hope this is not a duplicate post. I tried to find it but I have not found it. I hope that someone could help me with understanding the exercise. This question is about a vase with r red ...
0
votes
1answer
46 views

Question about Measure Theory [on hold]

Let $(\Omega, U, P)$ be a measure space and X be random variable and its distribution function $F_x(x)=P(\{\omega: X(\omega)\le x\})=P(-\infty , x]$ and the function F is continuous at x. If the ...
1
vote
1answer
35 views

interpreting wording of probability question

Two dice are rolled, and the sum of the face values is six. What is the probability that at least one ofnthe dice came up a three? I want to make sure that I am interpreting the language right when ...
2
votes
2answers
42 views

Martingale definition

To prove that one process is Martingale, generally we prove 3 things : 1) X is adapted. 2)$$ \mathbf{E} ( \vert X_n \vert )< \infty $$ 3) $$\mathbf{E} (X_{n+1}\mid X_1,\ldots,X_n)=X_n $$ I ...
1
vote
1answer
18 views

What is the relation between$ P(A|B)$ and $P(A|B')$ for both independent and not independent events?

Let $A$ and $B$ be two events. If they are independent, how are $P(A|B)$ and $P(A'|B)$ related, if at all? If they are not independent, how are $P(A|B)$ and $P(A'|B)$ related, if at all? I've noticed ...
3
votes
0answers
21 views

Seven-Card Stud with Random Hand Selection

I was recently confronted with a number—$2727707$, actually—that started a short train of thought while I was placed on hold. (This seems to happen quite often: both the observation of unusual ...
3
votes
2answers
33 views

Conditional probability of exponential random variable

This question comes directly from a chapter in Gut's "Intermediate Probability" that focuses on conditional probability. I'm using this problem as more practice solving conditional probability ...
5
votes
3answers
73 views

Suppose a city with Three type of coins ?!

in a city we have tree type 1 dollar, 2 dollar, 3 dollar of coins. we want to pay for a 20 dollar product. how many ways we can pay for a 20 dollar product, if the seller has no money and number of 1 ...
-1
votes
1answer
34 views

Marginal distribution of uniform distribution conditioned on poission?? [on hold]

Let $N$ be a Poisson distribution with parameter $\lambda$. Conditioned on $N$, let $X$ be uniformly distributed. What is the marginal distribution of $X$? ( this is one of my final exam problems ...
0
votes
1answer
31 views

Geometric Random Variables

I have a question that involves a certain criteria of a random variable as shown: The random variable $X$ has the distribution $Geo(0.2)$ and I would love it if someone could explain what the ...
0
votes
0answers
56 views

What is the probability that 5 randomly chosen cards in a deck add up to 40 or more? [on hold]

I have made a probability game, where you have to pull out any 5 cards without looking (from a deck of 52 cards), and if all five cards add up to 40 or more, they player pulling the 5 cards from the ...
2
votes
1answer
57 views

What's the probability that the first four children born are boys and the last two children born are girls?

I'm having some problems with determining how to calculate a question about the gender proportion in newborns in some random family. A family consists of 6 children. The probability of a boy being ...
0
votes
1answer
13 views

Variable drawn from a normal distribution

What exactly is the meaning of a "variable drawn from a normal distribution"? I know what a normal distribution is, but my main exposure to "variables" is from calculus, so I have a hard time ...