query: $X_n\rightarrow X$ in probability, but $\mathbb{E}(X_n)$ does not converge to $\mathbb{E}(X)$
positive_passages.docid: 26633
positive_passages.text: Does convergence in probability implies convergence of the mean?
negative_passages.docid: 141165
negative_passages.text: Probability of $p(x_1<x_2<\max(x_3,x_4))$
negative_passages.docid: 124382
negative_passages.text: Showing that $f_n:[0,1]\to\mathbb{R}$ when $f_n=nx(1-x)^n$ converges pointwise but not uniformly
negative_passages.docid: 141463
negative_passages.text: Convergence of $x_{n+1} = \frac12(x_n + \frac2{x_n}).$
negative_passages.docid: 155206
negative_passages.text: Convergence in probability: $\lim_{n\to\infty}\int_0^1\cdots\int_0^1\frac{x_1^2+x_2^2+\cdots+x_n^2}{x_1+x_2+\cdots +x_n}dx_1\cdots dx_n=\frac23$
negative_passages.docid: 153854
negative_passages.text: $X_{n}$ converges in probability, $f$ is continuous, $f(X_{n})$ converges in probability
negative_passages.docid: 83790
negative_passages.text: Why doesn't $d(x_n,x_{n+1})\rightarrow 0$ as $n\rightarrow\infty$ imply ${x_n}$ is Cauchy?
negative_passages.docid: 94066
negative_passages.text: Prove that: {$f_n$} converges unifromly to $f$ on $E$ as $n \rightarrow \infty$ if and only if $\lim_{n\rightarrow \infty} ||f_n-f||_u = 0$
negative_passages.docid: 92569
negative_passages.text: Showing that ${\rm E}[X]=\sum_{k=0}^\infty P(X>k)$ for a discrete random variable
negative_passages.docid: 105656
negative_passages.text: $\sum_{n=1}^\infty u_n $ converges uniformly on $[a,b]$, but $\sum_{n=1}^\infty |u_n| $ doesn't
negative_passages.docid: 115146
negative_passages.text: Problem with almost sure converges random variable with Bernoulli distribution.
negative_passages.docid: 95515
negative_passages.text: Is $x_{n+1}=\cos x_n$ convergent?
negative_passages.docid: 95450
negative_passages.text: Why does $\left(1+ 1/k\right)^k$ converge to $e$ as $k \to\infty$?
negative_passages.docid: 138964
negative_passages.text: Convergence in distribution with given rate implies convergence in probability
negative_passages.docid: 10208
negative_passages.text: Tetration convergence: prove $\lim_{x\rightarrow0} {}^{n}x = \begin{cases} 1, & n \text{ even} \\ 0, & n \text{ odd} \end{cases}$
negative_passages.docid: 61085
negative_passages.text: $(P_n)$ converges to p if and only if every subsequence of $(P_n)$ converges to p
negative_passages.docid: 17735
negative_passages.text: $X_n = \text{Bin}(n,\frac{\lambda}{n})$ for $\lambda > 0$. Show $M_{X_n}(t)$ converges to the MGF of Poisson($\lambda)$ as $n\rightarrow \infty$