# 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).

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19 views

### Does the invariant distribution depend on the initial distribution of a Markov Chain?

I have just learnt about the invariant distribution, and was wondering if such depends on the initial distribution of a Markov chain in anyway, and if so, whether the following is the correct ...
14 views

### Can you measure differences in self-similarity?

For background, I have a rudimentary understanding of self-similarity as it applies to observing network traffic as a stochastic process. I also have a robust mathematical background but not in ...
40 views

### Let $2k$ be an even integer number and $r+s=2k$. What is the probability that none of $r$ and $s$ is not prime? [closed]

Let that $k$ be an integer number and $S$ defined as: $$S=\lbrace (r_i,s_i)| r_i+s_i=2k, 1<r_i\leq k \leq s_i<2k-1 \rbrace$$ No, Let that choose an element of $(r_j,s_j)\in S$ randomly by ...
1 vote
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### Given bivariate bernoulli with an integral as a parameter prove that are marginally identically distributed and correlation is positive

So this is a question from a past exam. The joint density function is \begin{equation} \begin{aligned} P\left(X_1=x_1, X_2=x_2\right) & =I_{\{0,1\}}\left(x_1\right) I_{\{0,1\}}\left(x_2\right) \...
23 views

### Convolution of two PDF

I am probably overlooking like, all the important details, but when trying to work out how to take the convolution of two pdfs I am going as follows: according to https://en.wikipedia.org/wiki/...
37 views

### Question About Derivation of Variance of Kaplan-Meier Estimate of the Survival Function: Why is Degree of Freedom Not Removed?

The variance of a sample proportion $\hat{p}$ is given by $$\text{Var}[\hat{p}] = \frac{p(1-p)}{n}$$ where $n$ is the sample size and $p$ is the true probability of success. Now to the best of my ...
65 views

### Fisher Information Matrix for Weibull Distribution...

I wish to find the Fisher Information Matrix for the Weibull Distribution... I face two difficulties, I can't find any sufficient guide in internet to lead me to derive the Fisher Information Matrix.....
17 views

### Conditional distribution of multivariate normal random vector

To calculate the conditional distribution of multivariate normal random vector $(X,Y)$, since that for all $a \in \mathbb{R}$ the random vector $(X-aY,Y)$ is normally distributed, we can determine $a$ ...
30 views

### Need help calculating the density of $(a,b)X$ where $X$ has density $f$

I’m currently working on a problem where I need to calculate the density of $(a,b)X=(aX,bX)$ where $a,b>0$ and $X$ has density $f$ . However, I’m facing some difficulties as the Jacobian method, ...
55 views

### What is the value of favorable outcomes in probability distribution

the given question is this: In the ii) part what should be the probability that the age is a prime number given that the age is greater than 15 years. I have two contradicting methods of solving this ...
32 views

### Correct definition of random variable and (discrete) probability distribution?

I defined it as follows: Let us consider a random variable $X$ defined on a countable sample space $\Omega$ over $K$ possible outcomes, and $P(X)$ its discrete PD defined as the set of probabilities ...
53 views

### Find a function such that f(x)/P(X > x) is a constant.

What do you think of the following question? "Let X be a continuous random variable such that $P(X\le 0) = 0$. Let $f(·)$ be its probability density function. Suppose that $f(x)/P(X > x)$ is ...
22 views

### Derivation of gamma function to obtain the PDF from the CDF

if $Z$ is a continuous random variable taking values from zero to infinity having a gamma distribution with shape parameter $A$ and scale parameter $B$ with the following CDF \begin{equation} F_{Z}(z) ...
63 views

### $P(X\geq{5})$ in a continuous uniform distribution

I had an exam in which I think I selected the right answer but in the Quiz is wrong. It is a multiple choice problem that goes as follow: "The waiting time until a train passes is a uniform ...
23 views

### Find the distribution of $X|Y=y$ where X and Y look like a a bivariate poisson.

It isn't a bivariate Poisson precisely, but has a pmf of: $$\mathbb{P}(X=x, Y=y)=\frac{\lambda^y e^{-2 \lambda}}{x !(y-x) !} I_{\{0, \ldots, y\}}(x) I_{\mathbb{N}}(y), \lambda>0$$ When I tried to ...
55 views