# Tagged Questions

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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### UMVUE for $\theta^2$

Let $X_1,...X_n$ be a random sample with distribution $\text{Normal}(\theta,1)$. Find the UMVUE for $\theta^2$ What I´ve done so far: I have already shown that $T=\sum_{i=1}^nX_i$ is a complete ...
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### Flipping coins- percentages of heads vs tails

If i flip a coin multiple times and count the number of time it fell on heads and the number of times it fell on tails and keep a track of them. In how many flips on average will the delta between ...
27 views

### Checking if a coin is fair [on hold]

I want to check if a coin is fair (lands 50% of the times on each side). I flip that coin multiple times and count the number of times it fell on heads and the number of times it fell on tails and ...
31 views

### why probability is multiplied in finding out dependent probabilities?

Why is probability multiplied in case of dependent events? When we want to find out say, We take out a card from a deck of 52 cards and take another without replacing, We get the probability of ...
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### Existence of Joint Distribution from Overlapping Marginal Distribution

Suppose $x_i\in \mathbb{R}^{n_i}$ for $i=0,1,...,k$. For each $i=1,...,k$, suppose $F_i$ is a probability measure of $(x_0,x_i)$ on $\mathbb{R}^{n_0 + n_i}$. Assume all $F_i$ have the same marginal ...
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### Calculating the expectation of binomial distribution without calculating the summation

We know that expectation of a binomial distribution is $$\sum _{1}^{n}\left(\begin{array}{c}n\\ k\end{array}\right){p}^{k}{\left(1-p\right)}^{n-k}k = np$$ But while proving it, it is being written ...
383 views

### Three fives dice toss

If four dice are tossed, find the probability that exactly 3 fives will show ( answer to the nearest thousandth in the for 0.xxx)?
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### Help with proof that $E(G|a < G < b) \lt E(H|a < H < b)$ for truncated normal distributions

Consider two independent normally distributed random variables with equal standard deviations, $G\sim N (\mu_{G}, \sigma)$ and $H\sim N (\mu_{H}, \sigma)$ that are truncated between points $a$ and $b$....
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### Card Probability Without Replacement

So there are 15 cards total, 5 red, 7 orange, and 3 yellow. At random you pick 3 (no replacement). What's the probability of picking: 1) Exactly 2 Red? 2) Not more than one yellow? 3) One of each? ...
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### sampling requirements in probabilistic polynomial identity testing

In the Schwartz–Zippel algorithm for bounded error probabilistic polynomial identity testing, the main theorem is the following: For a non-zero multivariate polynomial $p(x_1,...,x_n)$ of total ...
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### Most likely order of independent normal random events

The problem I have is, given $n$ independent normal distributions describing the times that $n$ random events occur at, what is the most likely order that they will occur in? This questions follows ...
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### If you roll two six-sided dice, what is the probability that the dice add to 10 or higher?

When answering these sort of questions people mostly resort to diagrams and I'm wondering if there is a way to calculate the probability without going through each outcome, just solely on the given ...
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### probability/combinatorics question with marbles

An urn has 20 green out of 50 marbles. Draw all 50 marbles without replacement. Let X = # of green marble runs of any length. Example : GGGGBBBGGBBGBB. . . In the above example, there are 3 runs in ...
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### Average Goals Per Game

Okay I am trying to work something out. If for example Team A scored an average of 2.84 goals per game over a period of 95 matches. What is the probability that there next match will be 3 goals or ...
32 views

### Finding probability with the help of combinations

$N$ tutors are to be assigned to $s$ students with any student having at most one tutor and similarly any tutor having at most one student. If any tutor is assigned randomly then how can we find the ...
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### Suggestions for Constructing a Random Variables from Correlated Observations

Let $\mathcal{X} \neq \phi$ be a finite set. Let $P_{XY_1Y_2}$ be a fixed joint distribution over $\mathcal{X}\times\mathcal{X}\times\mathcal{X}\$ and that a random sample $(X,Y_1,Y_2 )$ is drawn ...
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### Loaded coin: probability I will never get two heads [on hold]

I'm currently starting to learn probability in an intro course in college and am wondering how to solve this. Given a loaded coin that gives a 60% chance of flipping heads, and 40% chance of tails, ...
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### Deriving global probabilities from local dynamics

I am interested in growth dynamics and, in particular, how to derive difference/differential/stochastic equations from local behavior of a system. For concreteness, let's imagine a simple predator/...
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### Probability Conjecture

I think there is a flaw in my logic but I'm not sure where it would be. Let HHH denote the event of three coin flips. Let E(HHH) be the expected value of the number of coin flips until HHH. Let E(...
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### Scale invariance of uniform distribution over $\mathbb R^2$?

If we make a uniform distribution of points over $\mathbb R^2$ with 1 point on average per unit square. And we zoom far out and make a density plot (give a color to each cell according to how many ...
27 views

### Value of c so that $c(2-|x|-|y|)$ is a probability distribution function(see picture)

Hint: Use the formula of volume of pyaramid. My approach: I know that the integral of a pdf from $-\infty to +\infty$ gives you $1$. I tried taking the double integral, but got stuck in as how to ...
633 views

### finding probabilty using Methods of Enumeration

A computer retail store has 12 personal computers in stock. A customer wants to purchase three of the computers. Assume that of the 12 computers, 4 are defective. If the computers are selected at ...
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### Expected length of a random walk

Let $G = (V,E)$ be a connected graph. Now consider a random walk on $G$, where we pick a random vertex $v_0$ sampled uniformly at random from $V$. Let $v_i \in V$ denote the vertex in the current ...
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### Why did my friend lose all his money?

Not sure if this is a question for math.se or stats.se, but here we go: Our MUD (Multi-User-Dungeon, a sort of textbased world of warcraft) has a casino where players can play a simple roulette. My ...
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### Find the MOM estimate and the MLE of the Pareto distribution.

The Pareto distribution has been used in economics as a model for a density function with a slowly decaying tail: Assume that $X_0$ > 0 is given and that $X_1, X_2, ..., X_n$ is an i.i.d. sample. ...
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### Two length 3 straights vs. one length 5 straight. Which is more likely and by how much?

Using a well shuffled standard $52$ card deck, $2$ players (call them A and B) decide to play a game. They draw community (shared) cards (without replacement) until a winner for that hand is ...
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### Probability of 20 consecutive success in 100 runs.

Suppose a chess player have a win rate equal 90%, what is the chance to have 20 consecutive wins (successes) playing 100 games? Consider that lose/draw = fail. I've studied basic statistics in ...
502 views

### probability - ice cream flavours [on hold]

Of the $50$ ice cream flavours at J.P. Lick’s, $10$ of the ice cream flavours have a vanilla base (as opposed to chocolate or some sort of other flavour base). Of the $50$ ice cream flavours, $15$ ...
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A die is loaded in such a way that the probability that a 6 is thrown is ﬁve times that of any other number, each of them being equally probable. What is the ratio of the probability of obtaining a ...
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### Transforming a categorical distribution by repeating trials and taking a plurality

Suppose you have a K-sided, weighted die. This is represented by a categorical distribution. Now, let's say you roll the die N times, and then pick a "winner" by choosing whichever outcome has a ...
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### Basic query Related to dependent random variables

$X$ and $Y$ are two dependent random variables. I want to find the following probability $$\Pr(2X<c,4Y>c)$$ wher $c$ is some positive number. In my attempt, I can expand the above probability ...