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Questions tagged [probability-distributions]

Questions on using, finding, or otherwise relating to probability distributions, probability density functions (pdfs), cumulative distribution functions (cdfs), or other related functions. Use this tag along with the tags (probability), (probability-theory) or (statistics).

Any probability distribution, including beta, binomial, chi, Erlang, gamma, geometric, lognormal, negative binomial, normal (Gaussian), Pareto, Poisson, Student's t, uniform, Wald, Weibull, zeta, and Zipf.

28080 questions
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PDF basic question

$p(x)=3x^2$ with $0 < x < 1$: 0 elsewhere. $p(x)$ is the probability density function of the variables. there are 3 independent variables $X_1$,$X_2$,$X_3$ with the distribution listed above What is the probability exactly 2 are greater than…
jason m
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Truncated distribution of a r.v. with multiple variables in the condition

Say we have two $i.i.d.$ random variables $X$ and $Y$ with support in $[0,1]$. We want to find $E[X| X > 0.7, Y > 0.7, \frac{X+Y}{2} > 0.9]$. This is given by: $\int x f(x|x > 0.7, y > 0.7, \frac{x+y}{2} > 0.9) dX $. What will be the expression…
Pradipta
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Probability with a uniform distribution

A group of athletes have pulse rates uniformly distributed between 60 and 75. What is the probability that a randomly chosen member of the group has a pulse rate greater than 70? I am thinking that because it is a uniform distribution, of interval…
UserX
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Combinations and Probability question?

You have to choose a committee of $5$ people. You have $13$ grade nines, $13$ grade $10s$, $13$ grade elevens and $13$ grade $12s$. $a)$ What is the probability that the committee chosen will be all of the same grade? $b)$ What is the probability…
Jessica
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Distribution of a compound Poisson distribution

I have to find the distribution of: $ \epsilon_t + \sum_{i=0}^{N_t}x_{i,t}$ where: $\epsilon_t$ follows N(0,1) $N_t$ follows P(0.1) $x_{i,t}$ i.i.d, follow N(-0.1,0.3) They are all independent. How would you calculate that ? (see what I have done…
Lucas Morin
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Sampling distribution of an estimator

All random variables here are iid. We have that $$f(x;\theta) = \alpha \mbox{ exp}\left[ -\alpha (x - \beta) \right] \times \mathbb{I} \left\{x \geq \beta \right\} $$ for $\alpha > 0$ and $\beta \in \mathbb{R}$. I have found maximum likelihood…
user117682
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exponential distribution expected value of all values greater than some value

Mean of exponential distribution is $$\frac{1}{\lambda}$$ What is mean of all samples greater than some value $S$? Some context: A DC power supply (as used in a telecommunications installation) has a battery of limited capacity $S$. A failure of AC…
philcolbourn
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Notation For CDF of Binomial Distribution

I recently downloaded a statistical distribution application on my android, and it lists the CDF for the Binomial Distribution as $I_{1-p}(n-k,1+k)$. I am not familiar with this notation, and I was hoping someone can explain it to me.
Russell
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Conditional expectation when throwing two dice

I throw two dice. The random variable X gives the result of the first die and the random variable Y gives the result of the sum of the two dice. What is the value of E(Y!X)?
user118601
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Does "2 bumps" in a histogram suggest 2 underlying populations?

I've plotted a histogram of data collected in real life, not generated data. It looks like a negative binomial binomial distribution with a 2nd bump, lower from the peak bump of the curve. Here is a screenshot: Question - is the second bump of any…
d l
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Gaussian random variable vs i.i.d. random variable

I have a random variable X, to which additive gaussian noise is added resulting in random variable Y. I have $\log \frac{X=-1|Y}{X=1|Y}$. This is equal to $\log \frac{P\left\{X=-1\right\} \cdot P\left\{Y|X=-1\right\} \cdot…
Rohit
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Calculate the probability mass function

I have the following problem: You have a standard deck of 52 cards. The cards: 2,3,4,5,6,7,8,9,10,J,Q,K,A J, Q, K, A have the values 11, 12, 13, 14 appropriately. Two cards are drawn from the deck without replacement. Let X be the absolute…
Ben Watson
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Distribution of the indicator function of a Gaussian variable.

Let $\xi$ be a random variable distributed according to a Normal distribution with given mean $\mu$ and standard deviation $\sigma$. Find the probability density function of $$ \psi = c\,\mathbb{1}_{\left\{\xi\leq 0\right\}}, $$ where…
AlmostSureUser
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Uniform continuous distributions - question with a square RV

Question: Jack wants to build a wooden cylinder, He decided to choose it's radius (Y) randomly s.t $Y\sim U[0,1]$. a. What is the probability that the radius is in a closed interval $[\alpha,\beta]$? what is Y's density function? b. What is the…
jreing
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Variance of empirical probability

A have a weighted die and I toss it $N$ times. The empirical probability of getting the $i^{\text{th}}$ face of the dice is: $$ P(i) = \frac{N_i}{N},$$ where $N_i$ is the number of times I tossed $i$ and $N$. Now, if I think of the empirical…
ponadto
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