Mathematics Stack Exchange
Mathematics Stack Exchange

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
1
vote
1 answer

How to calculate this joint PMF?

Consider three random variables X, Y, and Z, associated with the same experiment. The random variable X is geometric with parameter p∈(0,1). If X is even, then Y and Z are equal to zero. If X is odd, (Y,Z) is uniformly distributed on the set…
Q Yang
  • 349
1
vote
1 answer

Can anyone give me a hint how to start this one...

If the variance of the random variable X exists, show that $\mathbf{E}(X^2)≥[\mathbf{E}(X)]^2$. I don't know how to start, so any hint is appreciated. Thank you in advance.
kopara
  • 61
1
vote
1 answer

Not sure how to solve this probability problem...

From a well-shuffled deck of ordinary cards, four cards are turned over one at a time without replacement. What is the probability that the spades and red cards alternate? Is the solution…
kopara
  • 61
1
vote
2 answers

Sum of two non-identical independent uniform random variables

Let $X\text{~Uniform} [0,1]$ and $Y\text{~Uniform}[0,2]$. Find the distribution of their sum, $Z = X + Y$, using the convolution method. I understand that I have to break this into cases for $Z=[0,1],[1,2],[2,3]$, but I'm having difficulties…
ittiekat
  • 41
1
vote
1 answer

What kind of distribution is that?

Could you tell me what kind of distribution is that? I can also provide the original data if needed.
b9d
  • 11
1
vote
1 answer

Continuous random variable from Poisson distribution

X, which represents the number of emission from a radioactive substance in n seconds, follows a Poisson distribution with a mean of 3n. The first part of the question asks for an expression for the probability that there are no emissions in a…
theVerma
  • 49
1
vote
2 answers

Does strictly positive density function on the real line with infinite expected value exist?

The problem is as stated in the title. I am looking for an example or a disproof, whether there exists a continuous density function on the whole real line with infinite expected value. Once again: The density function $f$ must be $1.$ Positive on…
Seyhmus Güngören
  • 7,848
1
vote
2 answers

linear combination of random variables

Let $X$ and $Y$ be $iid$ uniformly distributed random variables over the interval $[0,1]$. We know by convolution that the distribution of $Z=X+Y$ is given by: $$f(z) = \left \{ \begin{array}{ccc} z & \text{if} & 0\leq z \leq 1 \\ 2-z & \text{if} &…
cgo
  • 1,810
1
vote
1 answer

Sum of a sum of regular normal distribution

Can someone please confirm if the solution below is correct? If not, please give me some hints about what is wrong. Let $X$ and $Y$ be two real valued stochastic variables who's joint distribution is the regular normal distribution on…
Rud Faden
  • 149
1
vote
1 answer

cumulative distribution function of a multivariate normal variable in a degenerate case

Let $X=\left[x_{1},x_{2},\cdots,x_{n}\right]^{T}\in\mathbb{R}^{n}$ be a multidimensional normal variable with the mean vector $\mu_{X}\in\mathbb{R}^{n}$ and the covariance $\Sigma\in\mathbb{R}^{n\times n}$, where $\Sigma$ is not full rank (the…
Van Long DO
  • 23
  • 3
1
vote
0 answers

Error analysis of kernel density estimation

Let $X$ be a random variable with true density $f$, $Y = \{y_i\}_{i=1}^n$ be a realization of a random variable in $d$-dimensional space $R^d$, and $\hat{f}$ is the density estimator of $Y$ using kernel density estimation. My question is what is…
topzhang
  • 11
1
vote
1 answer

Who can help me to interpret the following expression?

I don't understand the second line of the following expression. Why does he use conditional expectation? and can you explain the following calculation process to me? Thanks.
eric
  • 83
1
vote
1 answer

The time between process problems

The time between process problems in a manufacturing line is exponentially distributed with a mean of 30 days. (a) Let T be the waiting time (in days) for four problems. What is the distribution of T? (b) What is the expected waiting time for four…
Alistair
  • 271
1
vote
2 answers

Distribution whose PDF is proportional to the product of a PDF and a CDF

Let $\phi$ be a symmetrical probability distribution function, that is nonnegative, that means $\int_{-\infty}^\infty \phi(x) dx = 1$ and $\phi(-x) = \phi(x) \forall x$ and $\phi(x) \geq 0 \forall x$. Let $\Phi$ be it's cumulative distribution…
flawr
  • 16,533
  • 5
  • 41
  • 66
1
vote
2 answers

$X\sim U(0,1)$, $Y\sim U(0,2)$, how can I find CDF of $T=X+Y$ without knowing the joint PDF of $X$ and $Y$?

$X\sim U(0,1)$, $Y\sim U(0,2)$, how can I find CDF of $T=X+Y$ without knowing the joint PDF of $X$ and $Y$? Does anyone could help me with this?
user133140
  • 885
1 2 3
…
99 100