query: Suppose that the discrete random variable X can only assume values in the interval [0,1].
positive_passages.docid: 15872
positive_passages.text: How to prove a random variable taking values in $[0,1]$ range has variance no larger than $\frac{1}{4}$?
negative_passages.docid: 154706
negative_passages.text: Spacings between discrete uniform random variables
negative_passages.docid: 113255
negative_passages.text: $X,Y\sim U(0,1)$ are independent, $W=\max (X,Y)$.
negative_passages.docid: 45025
negative_passages.text: IID Random Variables that are not constant can't converge almost surely
negative_passages.docid: 41100
negative_passages.text: Density of sum of two independent uniform random variables on $[0,1]$
negative_passages.docid: 155311
negative_passages.text: How to get a set $E$ such that $0<\mu(E\cap I)<\mu(E)$ for all interval $I$?
negative_passages.docid: 127486
negative_passages.text: Probability of continuous random variable
negative_passages.docid: 61969
negative_passages.text: A basic question on Poisson random variable
negative_passages.docid: 54791
negative_passages.text: Is it true or false that $\lvert P([0, 1]) \setminus P((0, 1)) \rvert > \lvert P(\mathbb{N}) \rvert$
negative_passages.docid: 153393
negative_passages.text: Is there a *simple* example showing that uncorrelated random variables need not be independent?
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: 115146
negative_passages.text: Problem with almost sure converges random variable with Bernoulli distribution.
negative_passages.docid: 154091
negative_passages.text: Is there any counterexample to show that $X,Y$ are two random variables and $E(X\mid Y)=E(X)$, but $X$ and $Y$ are not independent.
negative_passages.docid: 75333
negative_passages.text: Is the limit of a sequence of random variables unique?
negative_passages.docid: 14063
negative_passages.text: Is a non-negative random variable with zero mean almost surely zero?
negative_passages.docid: 156092
negative_passages.text: Existence of independent and identically distributed random variables.
negative_passages.docid: 86729
negative_passages.text: Are squares of independent random variables independent?