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7h
answered Independence and expected value
8h
revised Relation between differential equations and sequence recursions
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8h
answered Relation between differential equations and sequence recursions
8h
revised Relation between differential equations and sequence recursions
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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
amazon.com/Calculus-Variations-Dover-Books-Mathematics/dp/… and amazon.com/Introduction-Calculus-Variations-Dover-Mathematics/…
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?
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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?
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