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 7h answered Independence and expected value 8h revised Relation between differential equations and sequence recursions added 145 characters in body 8h answered Relation between differential equations and sequence recursions 8h revised Relation between differential equations and sequence recursions added 9 characters in body 8h comment Automatic curve fitting? are you looking for specifically polynomial fits? in what environment - C, Excel, MATLAB, Python, etc? 8h answered Recurrence of 0 in a random walk 8h answered Number of truth tables for a 2 letter formula 9h revised Let $N=3^{1000}\times 2^{200009} +1$. Show that $5^{\frac{N-1}{2}}\equiv -1 \pmod{N}$. edited title 11h comment How to isolate and solve for k in a Sigma notation probability mass function equation? There is a mistake in your formula. It is supposed to be $$P(X = n) = \sum_{k=0}^n = {{{K \choose k} {{N-K} \choose {n-k}}}\over {N \choose n}}$$ and the question is asking to solve for $n$ 11h comment Finding a function of a random variable that maximizes some expression 11h comment Finding a function of a random variable that maximizes some expression optimizing for a function sounds like Calculus of Variations to me 11h comment Finding a function of a random variable that maximizes some expression you probably mean $$g(b_1(v_1),b_2) = \Pr (b_1(v_1) \geq b_2) \cdot \mathbb E(v_1 - b_1(v_1)).$$ Also why do you need $v_2$? 11h comment Geometric progression question. Year less? @Bradman175 does not really influence the answer -- yours is the correct one 1d revised What is the inequality which is used to prove this inequality? added 1 character in body; edited title 1d comment Convergence of $\sum_{i \leq n} X_i/n$ @Math1000 yes, otherwise use $Z_n = nY_n - n\mu_X$ where $\mu_X = \mathbb{E}[X]$... 1d comment Convergence of $\sum_{i \leq n} X_i/n$ $(nY_n)$ is definitely a martingale 1d revised Let $X$ and $Y$ be iid real-valued random variables. Show $P[|X-Y| \le 2] \le 3P[|X-Y| \le 1]$. edited tags 1d comment Let $X$ and $Y$ be iid real-valued random variables. Show $P[|X-Y| \le 2] \le 3P[|X-Y| \le 1]$. Here is a thought, but not sure how to finish it. $$\mathbb{P}[|X-Y| \le a] = \int_{-\infty}^\infty [F(y+a) - F(y-a)] f(y) dy$$ so in your case it suffices to prove that $$F(y+2) - F(y-2) \le 3 F(y+1) - 3F(y-1), \quad \forall y \in \mathbb{R}$$ but I am not sure how to prove this is in general. 1d revised Let $X$ and $Y$ be iid real-valued random variables. Show $P[|X-Y| \le 2] \le 3P[|X-Y| \le 1]$. edited title 1d revised Geometric progression question. Year less? added 7 characters in body