query: How to show $X_n$ converges in distribution to U(0,1)
positive_passages.docid: 154229
positive_passages.text: Convergence to a Uniform Distribution
negative_passages.docid: 144957
negative_passages.text: Uniform convergence of a function
negative_passages.docid: 88676
negative_passages.text: Proof verification : $X_n \to X$ in distribution, $Y_n \to 0$ in probability $\implies$ $X_nY_n \to 0$ in probability
negative_passages.docid: 157762
negative_passages.text: Showing $f_n(x):=\frac{x}{1+n^2x^2}$ uniformly convergent in $\mathbb R$ using $\epsilon-n_0$
negative_passages.docid: 148410
negative_passages.text: How do I show $f_n(x)=n^2 x^n(1-x)$ pointwise converges to $0$ on $[0,1]$?
negative_passages.docid: 153063
negative_passages.text: Uniform convergence of $f_n(x)=nx^n(1-x)$ for $x \in [0,1]$?
negative_passages.docid: 78168
negative_passages.text: Using the law of large numbers to show that $M_n=\prod_{k=1}^n (1+X_k)$ converges almost surely for $X_i$ i.i.d.
negative_passages.docid: 11942
negative_passages.text: show that $x$ is in $\ell^1$ if $\sum x_ny_n$ is convergent for all $y=(y_n)\in{c_0}$
negative_passages.docid: 57778
negative_passages.text: Convergence in Distribution of the maximum of a sequence.
negative_passages.docid: 115146
negative_passages.text: Problem with almost sure converges random variable with Bernoulli distribution.
negative_passages.docid: 68081
negative_passages.text: x/n uniformly convergent?
negative_passages.docid: 60282
negative_passages.text: Prove that $f_n$ converges uniformly on $\mathbb{R}$
negative_passages.docid: 141463
negative_passages.text: Convergence of $x_{n+1} = \frac12(x_n + \frac2{x_n}).$
negative_passages.docid: 30471
negative_passages.text: Show that $a_{n+1}= 1 + \frac{1}{a_n}$ converges.
negative_passages.docid: 122053
negative_passages.text: Convergence in probability of $Y_n = \frac{2}{n(n+1)} \sum_{j=1}^{n} jX_j$, given $X_1,X_2,...$ iid
negative_passages.docid: 113384
negative_passages.text: $\sum_{n\geq1} k_n x_n$ converges for every $x \in l_1$, then $\sup_{n\geq1} |k_n| < \infty$
negative_passages.docid: 132948
negative_passages.text: Prove if $\left\{x_n\right\}$ converges to $2$, then $\left\{\frac{1}{x_n}\right\}$ converges to $\frac{1}{2}$