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Questions tagged [probability]

For questions about probability. independence, total probability and conditional probability. For questions about the theoretical footing of probability use [tag:probability-theory]. For questions about specific probability distributions, use [tag:probability-distributions].

The probability that an event occurs is a number in the interval $[0, 1]$, which represents how likely the event is to happen. $0$ indicates it will never happen, $1$ indicates it will always happen.

For example, throwing two dice gives a total of $6$ five times out of thirty-six. We write $$P(X=6)=\frac{5}{36}$$.

Use this tag for basic questions about probability, independence, total probability and conditional probability.

For questions about the theory of probability, use instead. For questions about specific probability distributions, use .

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What's the role of $h(x)$ (base measure) in the definition of exponential family

While the correct definition of exponential family is $$ f_X(x\mid\theta) = h(x) \exp \left (\eta(\theta) \cdot T(x) -A(\theta)\right ), $$ it seems that in many materials I read, they don't pay much attention to $h(x)$. Sometimes, authors just…
zym1010
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Transformation of Random Variables

Suppose $f_{X}(x) = xe^{-x^2/2}$ for $x>0$ and $Y = \ln X$. Find the density function for $Y$. So we want to find $P(Y \leq y)$. This is the same thing as $P(\ln X \leq y)$ or $P(X \leq e^{y})$. Thus $f_{Y}(y) = f_{X}(e^y)$? Or does $f_{Y}(y) =…
NebulousReveal
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De Morgan's law in probability theory

I'm wondering if this holds $$\overline{(A\cup \overline{B})}=\overline{A}\cap B$$ I have this problem in probability theory, if $A$ and $\overline{B}$ are independent events then $\overline{A} $ and $B$ are also independent events. Can I use De…
vilbur
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Probabilities for clock visits based on coin flips

We have a fair coin, and start at the 12 o'clock marker on a clock. At each step, flip the coin. If heads, move clockwise, if tails move counter-clockwise. As you land on a number, mark that number as visited. Which number(s) on the clock has the…
Coin_problem_arm
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Russian roulette, how many people left

I have a questian about a game similar to russian roulette. Suppose that we have n people in a room. Every round, everyone shoots a random person. So it can happen that everbody dies, or if everyone shoots the same person only two people die(the…
Hank
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Variance of sums of independent random variables

I have the following formula - $Var(\overline{X}) = Var(\frac{1}{n}\sum_{i=1}^n X_i) = \frac{1}{n^2}\sum_{i=1}^n Var(X_i)$ I know that the variance of the sum of independent random variables is equal to the sum of the variances of the random…
csss
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Solve the problem using Chebyshev inequality

The problem is the following: The symmetric coin is tossed 1600 times. What is the probability that the head will be shown up more than 1200 times? Attempt. Using the formula $\mathbb{P}(|X-MX|)>e)≤ DX/e^2$ I put the numbers in…
saakian
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Question on distribution of the sum of indicator variable

Let $X_1,\dots,X_n$ are i.i.d random variables with geometric distribution, and the successful probability is $p$ for each $X_i$. So for any $X_i$, the probability mass function is $\Pr(X_i=k)=(1-p)^{k-1}p$ Define a list of indicator variables…
Fan Zhang
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Where am I doing it wrong? Trying to develop intuition for probability

I have two problems which I know how to solve now, but I am still not quite sure why my initial solutions are incorrect. I would really appreciate a thorough explanation of where I went wrong. Thank you. Problem #1: In a pond there are 105 fish, 40…
ZFCm
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What is the probability to win? Die game

You have a die. If you get one pip at any point in the game you lose. If you get two,..., six pips you start adding the number of pips to a sum. To win the sum must get greater or equal to 100. What is the probability to win the game?
Mazzer
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Probability - sum of two dependent binomial variable

If $X \sim B(n, p)$ and $Y \sim B(m, p)$ are dependent binomial variables with the same probability $p$, and same number of elements $N$, does that make $X + Y$ a binomial variable as well? If so with what parameters?
vondip
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Relationship between median and mean of a pmf

If you consider a distribution that has many medians: $$P(X=x) = \{(1, 0.25)(2,0.25),(3,0.25),(4,0.25)\} ,$$ we know that this distribution has multiple medians between $2$ and $3$ if we define a median as a number where $P(X \geq c) \geq1/2$ and…
lord12
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probability summation for an infinite sequence

Very simple case, but don't know how to prove say function $rand$ returns a uniformly sampled value in $(0,1)$ $x_0 = 1$ $x_1 = rand * x_0$ $x_2 = rand * x_1$ ... $x_n = rand * x_{n-1}$ Now the summation $S(n) = \sum_{i=0}^n x_i$ Is…
lulu
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problem requires condition probability

Q. A robot fires 3 shots at a moving target. For the first shot, the probability of hitting the moving target is 1/3. For subsequent shots beyond the first shot, the probability of hitting the moving target is 1/2 if the previous shot is a hit (for…
gary
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What's the probability of someone winning Warren Buffett's March Madness challenge?

Billionaire Warren Buffett is giving away $1 billion (references 1, 2, 3) to anyone who can pick a perfect March Madness bracket. Roughly speaking, what is the probability that Buffett will have to pay up?
James Faulcon
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