Newbetuts

if $X,Y$ be a random independent variables if $X+Y$ and $Y$ has the same distribution, then $\mathbb{P}[X=0]=1$

Is conditional probability also probability?

Using the Central Limit Theorem to show $\lim_{n \to \infty} \frac{1}{(n-1)!} \int_0^n x^{n-1}e^{-x} dx= 1/2$

Calculate the following limit using the Central Limit Theorem

Let $Y_1, \ldots , Y_n$ be independent with $Y_k \sim U(0,1).$ If $S_n=\Sigma_k kY_k$, show that $4S_n/n^2$ converges in distribution to $1.$

Choosing the correct subsequence of events s.t. sum of probabilities of events diverge

if $A$ subset of $B$ then $P(B)-P(A)=P(B\setminus A)\ge 0$

If the random variable $X$ is standard Cauchy then so is $1/X$

Formally, why does a logical contradiction have probability zero?

Prove that $P\Big( \bigcup\limits_{i=1}^{n}A_i\Big) = \sum\limits^n_{i=1}(-1)^{k-1}\sum\limits_{{i_k}=1}^n P (A_{i_1} \cap...\cap A_{i_k}).$

Case of equality in Markov's inequality

Using Borel-Cantelli to find limsup

Sum of two independent normal distributed random variables

Sum-Product of Random Variables

Percolation theory critical density simple proof!

New posts in probability-theory

The largest component of G(n, p)

$\mu \otimes \nu(A \times B)=\mu(A)\nu(B)$

Stochastic ordering when multiplying pdfs

Prerequisites on Probability Theory

How to calculate $ \mathbb{E}\left[X|W=0\right] $

if $X,Y$ be a random independent variables if $X+Y$ and $Y$ has the same distribution, then $\mathbb{P}[X=0]=1$

Is conditional probability also probability?

Using the Central Limit Theorem to show $\lim_{n \to \infty} \frac{1}{(n-1)!} \int_0^n x^{n-1}e^{-x} dx= 1/2$

Calculate the following limit using the Central Limit Theorem

Let $Y_1, \ldots , Y_n$ be independent with $Y_k \sim U(0,1).$ If $S_n=\Sigma_k kY_k$, show that $4S_n/n^2$ converges in distribution to $1.$

Choosing the correct subsequence of events s.t. sum of probabilities of events diverge

if $A$ subset of $B$ then $P(B)-P(A)=P(B\setminus A)\ge 0$

If the random variable $X$ is standard Cauchy then so is $1/X$

Formally, why does a logical contradiction have probability zero?

Prove that $P\Big( \bigcup\limits_{i=1}^{n}A_i\Big) = \sum\limits^n_{i=1}(-1)^{k-1}\sum\limits_{{i_k}=1}^n P (A_{i_1} \cap...\cap A_{i_k}).$

Case of equality in Markov's inequality

Using Borel-Cantelli to find limsup

Sum of two independent normal distributed random variables

Sum-Product of Random Variables

Percolation theory critical density simple proof!