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# 77 Accepts

 Jan28 accepted Show both relaxations of boolean LP give equal lower bounds Mar11 accepted Prove the set of sequences $c_0$ which converge to zero in $l_{\infty}$ is closed. Jan29 accepted Prove this matrix is invertible for $n < m-1$ Oct5 accepted Prove that $\frac{d}{dx}\int_0^xf(x,y)dy = f(x,x)+\int_0^x\frac{\partial}{\partial x}f(x,y)dy$ Sep25 accepted Let $b_n$ decrease monotonically to zero, prove $\sum b_nz^n$ converges for $|z|\leq 1$ and $z\neq 1$ Aug18 accepted Question on sufficient statistics Aug18 accepted Show that $(x+1+O(x^{-1}))^x = ex^x + O(x^{x-1})$ for $x\rightarrow \infty$ Aug15 accepted Calculating a probability mass function (sufficient statistic) Jul22 accepted Sampling 100 widgets to test for defective ones Jul6 accepted Prove that the number of ways to put $n$ distinct balls into $n$ distinct boxes is $n^n$ Jun4 accepted Understanding Conditional Expectation May29 accepted Rigorous proof that $\int_{\Omega}X\;dP=\int_{-\infty}^{\infty}xf(x)\;dx$ May29 accepted For $\mu(X)<\infty$ and $f_n<\infty$ a.e. s.t. $\forall M$ $\exists n$ s.t. $\mu(\{f_n>M\})\geq\delta$, then $f_n$ diverges on set of positive measure May25 accepted An alternate proof of Egorov's Theorem May17 accepted The semifinite portion of a measure $\mu$ May16 accepted Counterexample to upper continuity May8 accepted Using the Residue Theorem for a contour integral along the Riemann sphere Apr15 accepted Show that the countable product of metric spaces is metrizable Apr14 accepted Let $(X,\large\tau)$ be a normal topology, then show that the weak topology induced by the cont. real-valued functions on $X$ is $\large\tau$ Mar23 accepted Prove that the closed unit ball of $L^2[a,b]$ is closed in $L^1[a,b]$