Tagged Questions
1
vote
2answers
47 views
Expected value of ordered statistics
Random vector $(X,Y)\sim N(0,0,1,1,\rho)$, that is to say, the density function of $(X,Y)$ is given by
$$f(x,y)=\frac{1}{2\pi\sqrt{1-\rho^2}}\exp\left\{-\frac{1}{2(1-\rho^2)}(x^2-2\rho ...
1
vote
1answer
31 views
Probability of line intersecting the convex set.
I would like to prove this theorem:
Let $A,B \subseteq \mathbb{R} ^3$ be convex, limited sets. $B \subseteq A$. I have a "random line", which intersects A. Probability, that this line also intersects ...
0
votes
1answer
73 views
Finding the median value on a probability density function
Quick question here that I cannot find in my textbook or online.
I have a probability density function as follows:
$$0.04x \space 0 \le x < 5$$
$$ 0.4 - 0.04x \space 5 \le x < 10 $$
$$ 0 ...
0
votes
1answer
46 views
Independence between Uniform distribution and Exponential distribution question
I am trying to solve the following problem and I am having a great deal of difficulty in a number of areas. Help would be greatly appreciated!
Let me state the problem first.
If $X$ is uniformly ...
1
vote
1answer
33 views
Limits of Integration for marginal pdf
I just had a small question as something is bothering me.
I am trying to find the marginal pdf of the following joint pdf:
$f(x,y) = (1/8)(y^2 - x^2)e^{-y}$ where $-y \le x \le y$, $0 < y < ...
0
votes
0answers
69 views
Tight Upper/Lower bound for Incomplete Gamma function
Does anyone know of any tight upper/lower bound for incomplete Gamma functions? i.e either of the following functions:
$$
\Gamma(s,x) = \int_x^{\infty} t^{s-1}\,e^{-t}\,{\rm d}t
$$
or
$$
\gamma(s,x) ...
1
vote
0answers
81 views
Bayesian posterior with integrals over normal densities
Realizations from normal distributions with known precision are used to estimate the mean, but the realizations are not always precisely observed. Instead, only a range of the realization is observed. ...
2
votes
0answers
33 views
Average Bhattacharyya distance
Two conditional PDF's $f_1(y|X=x)\sim N(Ax,\sigma^2)$ and $f_2(y|X=x)\sim N(-Ax,\sigma^2)$ are given. I need to find their average Bhattacharyya parameter assuming $X$ has a Rayleigh distribution ...
1
vote
1answer
59 views
Calculate expected values for a normal distribution
Suppose that X ~ N(1,2)
Find:
$E(X-1)^4
and E(X^4)$
I have no idea how to get started. Do I just need to integrate the pdf of the normal distribution multiplied by what is between the brackets? If ...
0
votes
1answer
29 views
Find the moment generating function
$$f(y)=\frac{e^{-|y|}}{2}$$
I tried calculating it by integrating $(1/2)e^{ty}\cdot e^{-|y|}) dy$
and splitting up that integral into two separate integrals. However, I did not get a finite answer. ...
2
votes
1answer
41 views
Evaluate $Pr[Y - X < c, X \ge 0]$
Let $f(x,y) = Pr[X=x, Y=y]$ be the joint density of two random variables, $X$ and $Y$.
I have been given s = $Pr[Y - X < c, X \ge 0] = \int_0^\infty \int_{-\infty}^{c+y} f(x,y) dx dy $
I am a ...
0
votes
1answer
120 views
Probability: Determining Which Phone Plan Is Better
A consumer is trying to decide between two long-distance calling plans. The first one charges a flat rate of $10$ cents per minute, whereas the second charges a flat rate of $99$ cents for calls up ...
1
vote
0answers
47 views
Expected value of threshold function
Let $X$ be a random variable with probability density function $f(x)$, $\alpha>0$ a constant and $g(x)$ a function with $g(x)=\begin{cases}
\begin{array}{c}
g_{0},\\
g_{1}
\end{array} & ...
1
vote
1answer
40 views
Finding $EX$ of a density function (integrating $\ln u$ over infinity)
I've been given a density function as:
$f(x) = 1/4e^{-|x|/2}$ where $-\infty < x < \infty$
and need to show that $EX = 0$
I understand that to find $EX$ I must calculate $\int xf(x)~dx$ ...
0
votes
1answer
89 views
Erroneous Answer Key?
The problem I am working on is:
The current in a certain circuit as measured by an ammeter is a continuous random variable $X$ with the following density function: $f(x) = .075x + .2$ for $3 \le x ...
