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

finding the marginal density of Y

Question . The joint probability density function of X and Y is given by $f(x, y) = (1/8)(y^2 − x^2)e^{-y} , -y\leq x\leq y, 0\leq y \leq \infty $ Find the marginal density of x. So i know that we need to integrate out the Y from the joint PDF,and…
hazard
  • 425
1
vote
0 answers

Sampling distribution : mechanics of chi-squared variables

I try to understand the mechanics of the variables that are obeying to chi-squared distributions. To what distribution obey the square root of a chi-squared variable. For example, $\sqrt{X}\sim \,?$ where $X\sim\chi^2$ with a degree of liberty $ =…
wayland700
  • 111
1
vote
0 answers

Two levels of MLRP preserves stochastic ordering

Suppose, conditional on state $\theta \in \{0, 1\}$, there is a signal $x \sim F(x)$ which satisfy MLRP property. That is $\frac{f_1(x)}{f_0(x)}$ is increasing in x Now, we add another level of signal. That is conditional on x, there is a…
Saptarshi Mukherjee
  • 11
1
vote
1 answer

table reservation problem

I saw a table reservation problem which already being solved in the forum: Experience shows that 20% of the people reserving tables at a certain restaurant never show up. If the restaurant has 50 tables and takes 52 reservations, what is the…
samtck92
  • 19
1
vote
1 answer

Chi Squared Distribution with $\mu = 0$, $\sigma^2 \neq 1$

Let $X_i$ be independent normally distributed random variables with zero mean and variance $\sigma^2 \neq 1$. What is the probability density function of the random variable formed by the sum of their squares? Here is my attempt: Let $Y =…
Weaam
  • 2,849
1
vote
1 answer

Airline binomial distribution overbooking question

An airline has a plane with 400 seats. The probability that a passenger fails to turn up for their flight is 0.04. The airline has an overbooking policy. Find the largest number of passengers this airline can book and still be at least 85% sure…
user321652
  • 11
1
vote
2 answers

Simple proof on uniform distribution

We have two random variables, $X$ and $Y$. $X$ follows uniform distribution. If $Y = aX + b$, how is any particular percentile of the Y distribution related to the corresponding percentile of the X distribution? I know the answer is straight…
Joseph
  • 551
1
vote
2 answers

Let X be a random variable with $E(X^m) = (m+1)!2^m$,m = 1,2,3,..... Find the density of X.

Let X be a random variable with $E(X^m) = (m+1)!2^m$,m = 1,2,3,..... Find the density of X. I assumed it to be exponential and it turned out to be true. But i couldn't prove it.
maths lover
  • 3,344
1
vote
1 answer

Why is this wrong? PMFs

I was asked to find $P_{XY}(x,y)$ from the CDFs. I gave the answer as $P_{XY}(x,y)=F_{XY}(x,y)-F_{XY}(x-1,y-1)$. I was told that I was wrong. Can you please explain why?
user313384
1
vote
0 answers

Prove using moment generating function: $\mathbf{y}^T \mathbf{A} \mathbf{y} \sim \chi^2(a) \iff \mathbf{A}^2=\mathbf{A}$ and rank($\mathbf{A})=a$.

I'm trying to prove the following using the moment generating function: For $\mathbf{y}\in \mathbb{R}^n \sim \mathcal{N}(0,I_n)$, one has $\mathbf{y}^T \mathbf{A} \mathbf{y} \sim \chi^2(a) \iff \mathbf{A}^2=\mathbf{A}$ and rank($\mathbf{A})=a$. So,…
Lasse
  • 11
1
vote
1 answer

How can i find distribution of ceiling poisson

There is poisson random variable $X$ $$P(X=x)=\frac{\lambda^{x}}{x!}e^{-\lambda}$$ And define random variable $Z=\lceil \beta X \rceil$ ( $\beta$ is rational number which is lower than 1). How can i find distribution of $Z$.?
Kim
  • 179
1
vote
1 answer

Convergence in distribution - X/Y

If X(n) and Y(n) converges to X and Y in distribution respectively then does X/Y(n) also converge to X/Y in distribution? Prove or disprove. I feel that this is correct but have not been able to proceed at all with the proof. If I move to…
Govind Saran Gautam
  • 113
1
vote
2 answers

Distribution of arrival times in a Poisson process

I have a Poisson process so its inter-event times are exponentially distributed. Suppose I fix a time T, (=0, say), and ask what the distribution of the time of arrival of the first event after T is. How do I find this? Could I reason as follows?…
Thad
  • 11
1
vote
1 answer

Choosing the distribution

If in an experiment I have recorded the number of people, lets say $X$, alive at some time ($>0$), out of a sample of $n$ people, which is the best distribution for $X$ to use? The survival time of a single person is modelled as an exponential…
rogerdom
  • 33
1
vote
2 answers

Factorial moment of negative binomial

What's the factorial moment of negative binomial distribution, if $$ \Pr(X = k) = \binom{k+r-1}{k} p^k(1-p)^r$$ I tried it: $$ E\left[ \frac{X!}{(X-m)!}\right] = \sum_{k=m}^{\infty} \frac{(r+k-1)!}{(k-m)!} \cdot p^k = \sum_{k=0}^{\infty}…
user304251
  • 11
1 2 3
…
99 100