Tagged Questions
3
votes
2answers
52 views
Let $\{X_n\}$ be i.i.d integrable r.v.s, show that $\frac{1}{n}\max_{1\leq j\leq n}|X_j|\to 0 \quad \mbox{a.e.}$
This problem is an exercise in Probability theory,independence,interchangeable, martingale(Chow), exercise 4.1.10.
Let $\{X_n,n\geq 1\}$ be independent identical distributed integrable random ...
3
votes
0answers
39 views
How to show $nP\{|X|>n\}\to 0$ as $n\to\infty$, but $X$ is not integrable.
How can I construct a random variable $X$ such that: $nP\{|X|>n\}\to 0$ as $n\to\infty$, but $X$ is not integrable.
0
votes
1answer
24 views
Length of life of a fire detector
The length of life of a flame detector is exponentially distributed with paramater $\lambda=0.1/year$. Die number of events which activate the flame detector in an interval with length $t$ (heat, ...
0
votes
2answers
32 views
How to determine the conditional expectation $\mathbb{E}[x^2\mid y]$
If $[x,y]^{T}$ is a two dimensional Gaussian random variable with zero mean and
\begin{equation}
\mathbb{E}[x,y]^{T}[x,y]=\begin{bmatrix}
\sigma_x^2 & r_{xy}\\
r_{yx}& \sigma_y^2\\
...
