query: Prove that (1 − λ)F + λG is also a distribution function.
positive_passages.docid: 153646
positive_passages.text: Convex combination of cumulative distribution functions
negative_passages.docid: 136475
negative_passages.text: d'Alembert-like functional equation: $f(x+y)+g(x-y)=\lambda f(x)g(y)$
negative_passages.docid: 130916
negative_passages.text: Proving the identity functions is continuous iff $\tau_1\supseteq\tau_2$
negative_passages.docid: 14277
negative_passages.text: Proving $f(x)=x\cdot |x|$ is a bijection
negative_passages.docid: 3346
negative_passages.text: Proof that Conditional of Poisson distribution is Binomial
negative_passages.docid: 110495
negative_passages.text: $X_n \to X, Y_n \to c$ in distribution implies $X_n Y_n \to Xc$ in distribution
negative_passages.docid: 6410
negative_passages.text: Prove that $(ma, mb) = |m|(a, b)\ $ [GCD & LCM Distributive Law]
negative_passages.docid: 42366
negative_passages.text: Prove $\mathbb{P}(\sup_{t \geq 0} M_t > x \mid \mathcal{F}_0)= 1 \wedge \frac{M_0}{x}$ for a martingale $(M_t)_{t \geq 0}$
negative_passages.docid: 97119
negative_passages.text: Prove that $\prod_{i=1}^n(1+x_i)\leq \sum_{i=0}^n\frac{S^i}{i!}$, where $x_i\in\mathbb{R^+}$.
negative_passages.docid: 82591
negative_passages.text: Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
negative_passages.docid: 19245
negative_passages.text: Schwartz Distribution Theory: (Non-)Surjectivity of $f \mapsto f*f$ in $ \mathcal E '$
negative_passages.docid: 122481
negative_passages.text: proof of an identity for exponential function
negative_passages.docid: 149739
negative_passages.text: Prove: $f(t)\leq t+1$
negative_passages.docid: 40905
negative_passages.text: Prove $f(\sum^k_{i=1} \alpha_i x_i) \leq \sum^k_{i=1} \alpha_i f(x_i) $ for a convex function f
negative_passages.docid: 26207
negative_passages.text: If $f$ is a quadratic and $f(x)>0\;\forall x$, and $g= f + f' + f''$, prove $g(x)>0\; \forall x$
negative_passages.docid: 105700
negative_passages.text: Proving $\,f$ is constant.
negative_passages.docid: 98816
negative_passages.text: How to prove that $\{f+g<a\}=\bigcup_{r\in{\Bbb Q}}(\{f<r\}\cap\{g<a-r\})$?