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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8 views

What does $\mathbb{P}(d\omega)=dw$ actually mean?

I am currently reading S. Shreve's book Stochastic Calculus II, and I have a question regarding Example 1.6.4 (p.35-36) which describes a change of measure, but I am puzzled by the notation. ...
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1answer
12 views

Probability of random value being correct within X amount of tries,

Let's say I have 4 numbers: 1234 These numbers have a predetermined combination of 2 that is the correct value, which could be any of the following 16. (1 in 16 ...
1
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1answer
10 views

Show that the collection of all subsets of a finite sample space satisfies the 3 conditions to be called a collection of events.

As title. Suppose that the sample space $S$ of some experiment is finite. Show that the collection of all subsets of $S$ satisfies the three conditions required to be called the collection of events. ...
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0answers
26 views

What is the probability of receiving the different types of hands of cards? [on hold]

A deck of cards has 52 cards. There are four suits – hearts, diamonds, spades and clubs. There are 13 ranks – 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King and Ace. When playing poker the following ...
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3answers
49 views

A man has 5 coins in his pocket…

A man has 5 coins in his pocket. Two are double-headed, one is double-tailed, and two are normal. The coins cannot be distinguished unless one looks at them. a) The man shuts his eyes, chooses a ...
-3
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0answers
9 views

Expectation of Normal Distribution cdf [on hold]

let let X~Normal(0,1), F(x) is CDF of X, Y~Normal(mu, sigma), what is E(F (y))?
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1answer
11 views

independent increments property implies Markov property

Let $\{X_t\}_{t\in\mathbb R^+}$ be a stochastic process with values in $\mathbb R$. Suppose that $\{X_t\}$ has independent increments, namely for every $t_1<t_2<\ldots<t_k$ the random ...
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3answers
54 views

Mutually exclusive dices?

Suppose I have 3 dice. Each has some mechanism that can prevent other dice being in 2 if itself is 2 when they are rolled together. Now I roll the 3 dice at the same time. Then what is the probability ...
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0answers
11 views

Probability of flip more coins [on hold]

Assume the coin is fair (50% tail, 50% head). Player1 flips n coins, and player2 flips n + 1 coins. All the flips are independent. What's the probability of player2 flips more head than player1?
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1answer
31 views

Solitaire conundrum

I've wondered about this for years and hope you might be able to figure out the answer for me. If I played solitaire with an unshuffled pack, turned three at a time so I could only play every third ...
1
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1answer
28 views

Limit of random variables sequence

I need a clever way to find the limit of $$\frac{\sin(\pi X_1)+\sin(\pi X_2) + \dots + \sin(\pi X_n)}{n},$$ where $X_i$ are independent random variables with the distribution ...
2
votes
1answer
17 views

Existence of an exponential double integral (for the probabilists: Are the $L^p$-norms of Brownian local time integrable in the space variable?)

I have encountered the following integral and, with a lot of handwaving and some identities for Gaussian integrals (see for example ...
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1answer
37 views

Expectation of sum of $n$ random variables.

Let $X_1, X_2, X_3 \ldots, X_n$ be n random variables which take values from $\{+1,-1\}$ uniformly. Let $S_n$ be defined as $$S_n =|X_1+ X_2+ X_3+ \dots +X_n| $$ Find the expectation $E(S_n)$ of the ...
0
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1answer
13 views

How many initial possible pairings are there for a single-elimination ping-pong tournament involving $n$ players where $n=2, 4$, and $8$?

How many initial possible pairings are there for a single-elimination ping-pong tournament involving $n$ players where $n=2, 4$, and $8$? Probability class. Should be very simple, but I don't ...
1
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0answers
26 views

Dice Roll Probability

I think I am just doing something really dumb but I am having a hard time with this problem. Consider that one is rolling $n$ six-sided dice. We wish to calculate the probability that at least $m$ of ...
0
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0answers
20 views

For a set of size n, how many collections from the set include a particular element?

I'm stuck on a problem which can be simplified as below: Given the first 12 letters of the alphabet (A .. L), in how many collections of 4 letters do both 'A' and 'B' appear. I recognise that there ...
1
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1answer
11 views

Binomial distribution for number of family members

The question below is a part of a more complex question in probability theory. I can't get my head around why is my solution incorrect... So here it goes. Distribution of number of boys in a family ...
1
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1answer
22 views

Probability expected value for Poisson distribution

Here's something I have problem with: A proofreader checks mistakes in a book. He corrects the ones he could find and relays the book to the author. The author also checks his book for mistakes, ...
0
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1answer
40 views

Expected number of 1's before a 6 shows up [on hold]

I have the following problem. How do I compute the expected number of 1s that will be seen by throwing a fair dice until a 6 turns up?
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2answers
37 views

A random number of random variables, (expectation help)

everyone First a definition let $S_N = X_1 + X_2 \cdots + X_N$ where $X_i$'s are random variables and $N$ is also a random variable. Also assume that the $X_i$'s(integer valued),independent ...
1
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1answer
43 views

how to know how many victories need to qualify

I'm participating in a soccer tournament, and I'm on a group with 7 teams, in this group will be qualify 4 teams, and 3 teams will be eliminated. How to know how many victories need to qualify my ...
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0answers
39 views

please help, How to solve this Question? [on hold]

Two aero planes bomb a target in succession. The probability of each correctly scoring a hit is 0.3 and 0.2 respectively. The second will bomb only if the first misses the target. Find the probability ...
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3answers
55 views

Probability of rolling 3 mutually exclusive dice

Suppose I have 3 dice. Each has some mechanism that can prevent other dice being in the same number as itself when they are rolled together. Now I roll the 3 dice at the same time. Then what is the ...
0
votes
1answer
39 views

What is my mistake? Dependent Probability does not add up to 100%

I have a question. There is some event 'A' and an event 'B'. Event 'B' only takes place when event 'A' is true. (The outcome of event 'B' is otherwise not dependent on the outcome of event 'A'). ...
2
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0answers
24 views

Does this solution to find Expected Value makes sense?

The problems statement for question number 6 on this link. The solution is provided if we switch tabs. I have not idea how the distribution function is formulated for the question. PS : If you ...
0
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1answer
38 views

An inequality in martingale

Suppose $X_n$ is a supermartingale,for $\lambda>0$ ,we have the following inequality: $$\lambda\mathbb{P}(\inf_{n\leq k}X_n\leq-\lambda)\leq\int_{[\inf_{n\leq k }X_n\leq -\lambda]}(-X_k) ...
0
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2answers
45 views

Normal distribution in which 90% of samples are between 2.99 and 3.01; what is the standard deviation?

Steel rods are manufactured to be 3 inches in diameter but they are acceptable if they are inside the limit 2.99 inches and 3.01 inches. It is observed that 5% are rejected as oversized and 5% are ...
3
votes
1answer
21 views

Convergence of expected values as random variables converge almost surely

Let I have a sequence of random variables $X_n$ that converges to random variable $X$ almost surely as $n\to\infty$. How can I proof that $\lim_{n\to\infty}\mathcal{E}[X_n]=\mathcal{E}[X]$ where ...
-4
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1answer
35 views

Given that $3\mathsf P(A\cap B)=2 \mathsf P(A'\cap B) = \mathsf P(A'\cap B')$ and $\mathsf P(A\cap B)=3/5$, what is $\mathsf P(A\mid B')$?

$A$ and $B$ are two events such that, $\mathsf P(A\cap B)=3/5$. Given that $3\mathsf P(A\cap B)=2 \mathsf P(A'\cap B) = \mathsf P(A'\cap B') = x$. Find $\mathsf P(A\mid B')$. Attempt: $$P(B')=P(A ...
-1
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1answer
43 views

Probability statistics [on hold]

Three boxes, practically indistinguishable in appearance have two drawers each. Box 1 contains a gold coin in first and silver coin in the other drawer, Box 2 contains a gold coin in each drawer and ...
1
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2answers
26 views

Trouble getting probabilites for Bayes Theorem

I'm trying to think of a way to calculate the probability of P(A & B), where: A = {a company makes me an offer} e.g. 1/20 B = {I accept the offer} e.g. 1/5 Assuming that the denominator of the ...
-1
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0answers
73 views

Determining the expectation of Distance [duplicate]

There are 2 circles,one placed at (-R,0) and other placed at (R,0).There are 2 points,one lying on the center of 1st circle and other lying at any point on the circumference of 2nd circle.What will be ...
1
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1answer
32 views

Can this function be a density function of a continuous random variable X?

F(x) = 0, if x < 1 F(x) = 1, if 1<=x<=2 F(x) = 0, if x>2 I think it could be, as long as the integral is 1. Any ideas?
8
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2answers
359 views

Contradictory recursion

I encountered this problem which I find very contradictory to my intuition. Could anyone enlighten me why my recursive formulation is wrong? "Roll a fair dice until the game stops. The game stops ...
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0answers
16 views

Variance Reduction by conditioning: How to know over what variable to condition?

I have a question related to variance reduction by conditioning. If I have to RV´s $X$ and $Y$ with means $1$ and $2$ respectevely and I want to approach the value of $P(X+Y \gt 4)$ by simulating. ...
1
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1answer
39 views

proof about sigma-algebra

The question is that, $f$ is a function mapping $\Omega$ to another space $E$ with a $\sigma$-algebra $\varepsilon$. Let $\mathbf{A}= \{A\subset\Omega : \text{there exists } B \in \varepsilon \text{ ...
1
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1answer
30 views

Solve $dX_t = (\sqrt{1+X_t^2} + \frac{1}{2}X_t) \, dt + \sqrt{1+X_t^2} \, dW_t$ explicitly

Solve explicitly the 1-dimensional equation: $dX_t = (\sqrt{1+X_t^2} + \frac{1}{2}X_t)dt + \sqrt{1+X_t^2}dW_t$ I have hopelessly been guessing solutions to this. Does anyone know how to solve this ...
0
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1answer
31 views
0
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2answers
37 views

Conditional probability: At least 3 kings given there are at least 2 kings in the hand of 13.

My first "conditional probability" problem. Sorry for all the questions. My instructor doesn't make sense to the class. A hand of 13 cards is to be dealt at random and without any replacement from an ...
0
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1answer
32 views

The probability of having $k$ successes before $r$ failures in a sequence of independent Bernoulli trials

Problem Find the probability of having $k$ successes before $r$ failures in a sequence of independent Bernoulli trials with $p$ being the probability of success. I thought of using the Binomial ...
1
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2answers
41 views

5-letter strings using the letters in the word “EVERGREEN”

From the word EVERGREEN, 5 letters are chosen at random and arranged into a string of letters. What is the probability that this string is palindromic?
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3answers
44 views

Variation of Monty Hall problem [duplicate]

On a game show, the Monty Hall problem is being played. The contestant is told to pick a door, and he does, but just before being able to tell the host which door he picked, one of the doors that the ...
2
votes
2answers
36 views

formula for infinite sum of a geometric series with increasing term

I'm looking for the Expectation of the discrete random variable X, E[X], with pmf: $$p(x)=(\frac 16)^{x+1}, x=0,1,2,3...$$ so what I tried is as follows... $$E[X]= \sum_{0}^\infty xp(x) =$$ so then ...
0
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2answers
22 views

probability, 2 chips drawn have either same number or color

I've viewed similar problems to this, but I'm not understanding the logic to the question and answers behind them. There are 5 red chips (each numbered 1, 2, 3, 4, & 5), and 3 blue chips (each ...
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3answers
31 views

Probability You Choose at least one chip of every color

There are 16 chips: 6 red, 7 white, and 3 blue. 4 chips are selected randomly and are not replaced once selected. What is the probability that at least one chip of every color is selected? I'm not ...
-2
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0answers
198 views

Expected value of the distance between the points on cirlces [on hold]

Moderator's note: This is a live contest problem from CodeChef. Per usual protocol this question will be locked until the end of the contest period. There are two circles of radius R on a ...
1
vote
3answers
19 views

Probability question with two groups of students

Thirty percent of the students in a calculus course and 20 percent of students in a statistics course receive A's. Furthermore, 60 percent of the students with an A in calculus receive an A in the ...
6
votes
2answers
468 views

How to solve 0.5 choose 4?

I was solving this problem for homework. It says, in the problem, that if n is positive you use the generalized definition of binomial coefficients. In my case, n is positive so I just plugged n= 0.5 ...
0
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0answers
31 views

Probability/Permutations [on hold]

In a 5-team tournament, each team plays one game with every other team. Each team has 50% chance of winning any game that it plays (there being no ties). Find the probability that the tornament will ...
0
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0answers
31 views

The moment generating function of the geometric distribution

For geometric distribution, a random variable $X$ has a probability mass function of the form of $f(x)$ where $$f(x)=p(1-p)^{x-1}$$ For it's moment generating function $$M_X(t)=E(e^{tX})=\frac{p ...