Questions tagged [density-function]
For questions on using, finding, or otherwise relating to probability density functions (PDFs)
2,331 questions
3 votes
0 answers
27 views
Gaussian tails for the density of the solution to an SDE driven by a fractional Brownian motion
Let $B^H$ be a one dimensional fractional Brownian motion with Hurst parameter $H\in(0,1/2)$ defined over a complete filtered probability space $(\Omega,\mathcal{F},(\mathcal{F}_t)_{t\ge 0},\mathbb{P})...
0 votes
1 answer
41 views
Is it possible to draw 2d density plot only knowing totals in any cross line
So we see from the density plot that the most dense part happens to be intersection of the x, y histograms where the highest bar meet. But suppose we only have the x, y histograms, I think it's not ...
- 203
0 votes
4 answers
85 views
Why is the mean of a piecewise probability density function the sum of the mean of both separate intervals?
I am doing probability density functions for Calculus 2 and came across a problem where I had to find the mean for a piecewise function. I looked up how to find the mean in this case and the equation ...
- 11
5 votes
1 answer
121 views
Pointwise limit of a sequence of density functions
I am trying to prove that the following sequence of density functions $$f_{n}(x) = \mathbb{1}_{\left(0,2^{n}\right)}(x) \cdot \left(\dfrac{\left(n\ln(2) - \ln(x)\right)^{n}}{2^{n}\cdot n!} \right)$$ ...
- 195
1 vote
3 answers
182 views
confusion about densities of a recursively defined sequence of uniform random variables
This is a follow up question to this question in which the following was asked: Let $\left\{X_{n}\right\}_{n\in \mathbb{N}}$ be random variables such that $X_{0} \sim \text{Unif} \left(0,1\right)$ ...
- 889
-2 votes
1 answer
44 views
Expected value of a transformed absolutely continuous random variable
I am trying to prove this theorem: Theorem 1. Given $X$ an absolutely continuous random variable with density $f_X$ and $Y=g(X)$ a transformation, we have that the expected value E[Y] of $Y$ is ...
- 61
7 votes
4 answers
3k views
Can a probability density function not integrate to 1 over its support?
I don’t know much Probability Theory beyond the undergraduate level. I was trying to model a simple scenario with my family. What is the probability I will develop type 1 diabetes in the following ...
- 657
2 votes
1 answer
120 views
Finding a density function for the minimum of two uniformly distributed random variables. [duplicate]
Problem: Let $Y_1$ and $Y_2$ be independent and uniformly distributed over the interval $(0,1)$. Find the probability density function for the following: $$ U = \min\left(Y_1,Y_2\right) $$ Answer: Let ...
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