# All Questions

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### Prove that if $E(X\log X)<\infty$ then $E(\sup_n |S_n|/n)<\infty$.

This is part 2 of a two part question. In the first part, we were asked to show that if you had a non-negative sub martingale $M_n$ then $$\sup_n E(\sup_{k\leq n} M_k)\leq \sup_n 2E(M_n \log M_n)+2$$ ...
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### Prove that $d(x,y)=\sum_{i=1}^\infty \frac{|x_i - y_i|}{2^i}$ converges

Question: Let S be the set of sequences of $0$s and $1$s. For $x = (x_1, x_2, x_3, ...)$ and $y = (y_1, y_2, y_3, ...)$. Define $d(x,y)=\sum_{i=1}^\infty \dfrac{|x_i - y_i|}{2^i}$ Proof the ...
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### How can I show that $f$ must be zero?

Let $f(x)$ be continuous on $[a,b]$ and suppose $\int_a^b f(x)g(x)dx = 0$ for every continuous function $g$ on $[a,b]$. Prove that $f(x)=0$ on $[a,b]$. I understand that $f(x)$ must be zero ...
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### Finding neccesary and sufficient condition for uniqness of neighbours on graph

Let $(G,E)=(V_1\cup V_2,,E)$ be a bipartite graph. Find necessary and sufficient condition s.t for every vertex in $V_1$ exist two unique neighbors from $V_2$. That seems obvious (necessary) that ...
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### Xavier spent less than of an hour walking home from school. Which fraction is less 5 2 than ? 5 5 F 7 3 G 4 5 H 10 2 J 9 [on hold]

math is a awesoma and very creative subject.Please help me with this particular question. Thank yo very much
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### Integration Convergence/Divergence Questtion

$$\int\limits_0^{\pi} \frac{ dt}{\sqrt{t} + \sin t }$$ How can one tell if this integral converges or diverges? Integral of $1/(\sqrt{t}+\sin(t))$ from $0$ to $\pi$. I can't even find the ...
I have three equations: $$X_m = \beta_0 + \beta_1 \cdot X_I + \varepsilon_{BL}$$ $$W_M = X_M + \varepsilon_{MBL}$$ $$W_I = \gamma_0 + \gamma_1 \cdot X_I + \varepsilon_{RDI}$$ The $\varepsilon$'s ...