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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-1
votes
0answers
27 views

Odds for rolling specific faces on a 3-sided die [on hold]

Firstly, thank you for taking my question! Imagine five (5) $3$-sided dice, so three unique faces. What are the odds (percentage) of rolling $3$ of the same face when rolling $5$ dice? When rolling ...
-5
votes
1answer
26 views

lottery question [on hold]

for the lottery -- if I have 4 numbers How can I see all of the 4 number combinations, never using the same number more than once in each combination
-3
votes
2answers
45 views

100-sided dice was rolled 98 times, how do you choose next numbes to bet, based on current outcomes.

100-sided dice was rolled 98 times, Numbers form 1 to 50 were rolled exactly once, except number 25, which wasn't rolled yet. Number 75 was rolled 49 times You can only bet if the next roll result ...
2
votes
3answers
269 views

Is the limit of càdlàg functions càdlàg?

Is the pointwise limit of càdlàg functions càdlàg? If not which are the weaker conditions to assure it? I cannot find a counterexample
0
votes
1answer
20 views

Is there an upper bound for expectation of product of two measurable function on a random variable?

I wonder if there is an useful upper bound for $\mathbb{E}_{x\sim p(x)}[f(x)g(x)]$ in the following form: $$ \mathbb{E}_{x\sim p(x)}[f(x)g(x)] \leq \mathbb{E}_{x\sim p(x)}[f(x)]\times xxxxxx $$ The ...
-2
votes
0answers
46 views

Probability - There is a radar, a computer and a gyroscope

There is a radar, a computer and a gyroscope on board an airplane. The probability that the radar fails is 0.2. If the radar fails, the gyroscope will also fail, and the probability that the computer ...
3
votes
2answers
70 views

Combinatoric Birthday Paradox

There is likely a closed form solution for this problem but it's had me puzzled for days. This is about a variant on the classic birthday paradox. To recap, the birthday paradox is where given only 23 ...
-1
votes
1answer
14 views

Distribution of specific distributions

I have a normal distribution of independent variables, and there are a specific number of samples to this distribution: say 1 million samples. A function is set by the largest value of these million ...
-2
votes
0answers
21 views

Scrabble/words with friends [on hold]

How many letter combinations are possible with 7 tiles? Just the math answer please, 7 tiles in 7 slots, how many different combinations? Thank you :)
0
votes
2answers
27 views

Why is this counting function finite? (It is used Probability)

Why is this counting function finite? I don't understand this interpretation of the author. Can you explain more about this? Please.
0
votes
0answers
23 views

Distribution of the test statistic?

Let $\mathbf{x}_i \sim \mathcal{N}(\boldsymbol\mu, \boldsymbol\Sigma)$. I am trying to find a distribution of the following test statistic $ T(\mathbf{x}) = \frac{\bar{\mathbf{x}}^H ...
0
votes
0answers
12 views

Meaningful Extreme value distribution

Extreme value theory (EVT) dictates that the limit distribution of the minimum of the set of i.i.d. Chi-square random varibales $\{C_1,C_2,\cdots,C_n\}$ is Weibull. The Weibull distribution has ...
0
votes
3answers
32 views

Probability of picking a card one out of 52 times.

Let's say we have a standard deck of 52 cards. What would be the probability of choosing the 2 of diamonds? Obviously, it would be $\frac{1}{52}$. If we were to randomly choose another card from ...
0
votes
0answers
16 views

An optimization problem for non-homogenous poisson process with unknow distribution

Jobs arrive at an M/M/1 type server according to an non-homogenous Poisson process with rate parameter $\lambda_k$. Where $\lambda_k$ and $\mu_k$ denotes the arrival rate and service rate at $k_{th}$ ...
0
votes
1answer
28 views

Probability that one normal Random Variable will fall within a given range of another.

I'm struggling with the following problem: (ed: Don't be lazy. Just type it out. ) A certain small freight elevator has a max. capacity $C$, which is Normally distributed, with mean ...
0
votes
1answer
23 views

Probability of 2 students being chosen the both have under 100 books at home

Suppose we select two students at random from the class of fifteen. What is the probability that both students chosen have less then 100 books at home? Data provided is the amount of books each ...
1
vote
1answer
13 views

Relationship between minimizing a conditional variance and a covariance

We are working with discrete-time stochastic processes. Let $v_k$ be a $\mathcal F_k$-predictable process, and let $X_k, \eta_k$ be $\mathcal F_k$-adapted processes. Define $V_k = v_kX_k+\eta_k$ and ...
-2
votes
2answers
35 views

How to solve this probability formulation? [on hold]

$\int_{200}^{250} P(a=x \land 450-x \leq b \leq 250)\space dx$, where $a$ and $b$ are uniformly distributed random variables on $(0,250]$ and $(10, 250]$ respectively.
3
votes
1answer
40 views

Probability question from GRE subject test

I ran across the following problem while practicing for the GRE math subject test: Suppose $X$ is a discrete random variable on the set of positive integers such that for each positive integer $n$, ...
-1
votes
0answers
33 views

How to calculate $P(X_1 < X_2 < X_3…X_n ) $ [on hold]

Could you please help with the following problem i am having- I need to calculate the probability of $X_1$ (randomly selected discrete value between $a$ and $b$) being smaller then $X_2$ (randomly ...
1
vote
2answers
35 views

Find the following probability

A bowl contains 16 chips, of which 6 are red, 7 are white and 3 are blue. If four chips are taken at random and without replacement, find the probability that there is at least 1 chip of each colour. ...
2
votes
2answers
53 views

Probability distribution of number of waiting customers in front of a counter

The number of customers arriving at a bank counter is in accordance with a Poisson distribution with mean rate of 5 customers in 3 minutes. Service time at the counter follows exponential distribution ...
0
votes
0answers
29 views

Show that the following set function is not a probability set function

If the sample space is $\mathfrak{C} = \{c : -\infty < c < \infty\}$ and if $C \subset \mathfrak{C}$ is a set for which the integral $\int\limits_C e^{-|x|}dx$ exists, show that this set ...
2
votes
2answers
25 views

Distribution of a product of Multinomials

Consider the following: $(X_1, X_2, X_3, X_4) \sim \mathrm{Multinomial} (n,\mathbf{p})$ where $\mathbf{p} = (p_1,p_2,p_3,p_4)$. I would like to find the distribution of $X_1 X_4$, or at least know ...
1
vote
1answer
31 views

Definition of standard deviation and $l_2$

If we denote the mean as $\mu$, then the standard deviation is: $$\sigma\equiv\left(\sum_{x\in X}{p(x)(x-\mu)^2}\right)^\frac{1}{2}$$ In other words, $\sigma$ is the average $l_2$ distance from $\mu$. ...
4
votes
2answers
56 views

How to take into account uncertainty on number of events

Suppose I generate a set of events $X_{i}$ for $i = 1,2 \dots N$ and suppose every event is either a success or a failure, ie. $X_{i} = 0, 1$. If $N$ is fixed, the MLE for the probability of success ...
0
votes
3answers
33 views

Confused about definition of absorption probability

My confusion can probably most easily be explained with an example. Consider the following one step transition matrix : $$ P=\matrix{% & 0 & 1 & 2 & 3 & 4 \\ 0 & ...
1
vote
1answer
33 views

“Time until arrival/departure” in a Poisson process…

Customers are served at a bank with the following process. While there is at most one customer in the bank, there will be only one person teller at a window. If a second customer comes into the ...
1
vote
2answers
32 views

For what fixed interest rates is a certain single-period, finite-state market arbitrage free?

A single period market with three states of nature $\omega_1$, $\omega_2$ and $\omega_3$ is given, in which a single asset is available, namely a stock that is worth $8$ units today, and whose payoff ...
1
vote
1answer
23 views

Rewriting probabilities as expectation

Consider the stopping time $\tau_a:=\lbrace{t>0| W_t >a\rbrace}$, where $W_t$ is a Brownian Motion. Define: $X_t:=W_{\tau_a+t}-W_{\tau_a}$. We have that $X_t$ is a Brownian Motion independent ...
-1
votes
1answer
39 views

A related problem regarding Normal Distribution (Continuous Probability) [on hold]

A circus performer who gets shot from a cannon is supposed to land in a safety net positioned at the other end of the arena. The distance he travels is normally distributed with a mean of 140 feet and ...
-1
votes
2answers
49 views

Question on Probability 11 [on hold]

The probability that $A,B$ and $C$ can solve a problem are ${4}\over{5}$,${2}\over{3}$ and ${3}\over{7}$ respectively . The probability of problem being solved by $A$ and $B$ is $8\over15$,$B$ and $C$ ...
0
votes
1answer
28 views

How to find the probability of declaring faulty

My question: Consider a company that assembles computers. The probability of a faulty assembly of any computer is $x$. The company therefore subjects each computer to a testing process. This testing ...
0
votes
1answer
39 views

Coin Toss Experiment

I conducted an experiment where I tossed a coin 100 times. I am assuming that the coin flips heads with a probability p=0.5. So that the coin is fair with a level of significance of 5%, I want to find ...
-1
votes
1answer
34 views

Probability for a game move [on hold]

There is $25\%$ chance that this skill activates the stun ability for each hit. The skill hits $4$ monsters and each monster is hit $4$ times , for a total of $16$ hits (each monster is hit $4$ times ...
3
votes
4answers
53 views

Binomial distribution, given the number of success, what is the expected total number of trials?

For a random variable that follows binomial distribution, $X|N=n\sim Binomial(n,p)$. What is the expectation of $N$ when we know the value of the random variable but don't know the total? ie. What is ...
2
votes
2answers
36 views

The Probability one Player will have more Kills than another based on a distribution of Kills? [on hold]

Alright, I'm definitely not a math guy so bare with me. I'll make this short and simple. I have a dataset of players and the # of kills (video game) they have per game. For instance, if there are 10 ...
2
votes
2answers
54 views

What conditional independence theorem is being used here

In stanford's machine learning lecture 1, linear regression is defined on page 11, section 3 as: For $i = 1, \ldots, m$, $y^{(i)} = \theta^T x^{(i)} + \epsilon^{(i)}$, where $\epsilon^{(i)}$ are IID ...
1
vote
1answer
21 views

Modelling a compound random variable from a Poisson process?

One other question I came across that I didn't quite understand. The number of forks that enter the sink follows a Poisson process with rate $λ= 200$ per month. Each fork which enters the sink ...
0
votes
2answers
36 views

Probability Uniform Distribution Set Up Integral

Consider a $1$ meter stick and suppose you break it into two pieces $X$ meters from the end, where $X \sim \operatorname{Unif}(0,1)$. What is the expected length of the longer piece (after it is ...
-2
votes
1answer
22 views

The probability that two randomly selected $2$ year old male feral cats will live to be $ 3$ years old is? [on hold]

The probability that a randomly selected $2$ year old male feral will live to be $3$ years old is $0.82666$. (a) what is the probability that two randomly selected $2$ year old male feral cats will ...
0
votes
1answer
25 views

Suppose that $E$ and $F$ are two events? [on hold]

Suppose that $E$ and $F$ are two events and that $P(E\cap F)= 0.4$ and $P(E)= 0.8$. What is $P(F\mid E)$ ?
3
votes
5answers
119 views

Uncountable increasing family of $\sigma$-algebras

Could someone give an example of what an uncountable increasing family of $\sigma$-algebras $\{\mathcal{F}_t\}_{t\geq 0}$, $(\mathcal{F}_s \subset \mathcal{F}_t$ for $s<t)$ might look like? For ...
3
votes
2answers
40 views

Poisson process conditional probability problem

Penguins slide through a chute in a Poisson process at a rate of $2$ per minute. Each penguin has a $10$% chance of being an emperor penguin, independent of everything else. Given that $90$ ...
2
votes
2answers
29 views

Probability Distribution

I'm thinking about a set of n users on Facebook. Between each of the $\binom{n}{2}$ pairs of distinct friends, lets say an edge (indicating that the two people are friends) is independently present ...
0
votes
2answers
41 views

Probability and integration

Compute $E[e^{tX}]$ where $X ∼ \mathcal{N} (0, 1)$. [Hint: Complete the square in the exponent.] Do we set up the integral from $0$ to $1$? Then how do you solve this integral?
0
votes
0answers
29 views

Probability Problem - Using Bernoulli trials

This is a question on review for an upcoming test, any suggestions on solving or steps to find the solution would be greatly appreciated. "Angela thinks that if you spin a penny, it will land heads ...
1
vote
1answer
39 views

Continuous distribution and independence [on hold]

Problem: In a room, there are 4 boys from high income families, 6 girls from high income families and 6 boys from low income families. How many girls from low income families also need to be present ...
2
votes
0answers
52 views

Of strings and substrings: A problem of probability

Problem Let $\Sigma=\{a, b\}$. Let $\Sigma^*$ denote the Kleene star of $\Sigma$: \begin{equation*} \Sigma^* = \{\varepsilon, a, b, aa, ab, ba, bb, aaa, aab, \ldots\} \end{equation*} where ...
1
vote
0answers
25 views

Randomly searching a maze with a given probability distribution function

Consider a 2d maze in which there is one entrance and one exit. You are not a good maze solver so starting at the entrance, you try to find the entrance by naive random depth first search with ...