Friday, 2 November 2018

probability - Randomly picking cards from deck with replacement

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If I randomly pick 80 cards, uniformly, from a standard 52-card deck, with replacement, what is the probability that every card is drawn a...

real analysis - Find a bijection between 2 intervals

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So I'm supposed to find a bijection between $[0,1) \longrightarrow [0,1]$. My attempt of solution is the function defined as $$f(x):=\be...

measure theory - How to determine if a random variable is $mathcal F$-measurable?

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For example : Consider the state space $\Omega = \mathbb{R}$, the $\sigma$-algebra, $\mathcal{F} = \{(-\infty, 0], (0, \infty), 0, \mathbb{R...

equivalence relations - fine the inverse of $[2]$ and $[23]$ in$ mathbb{Z}_{41}$

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I know the inverse of [23] is [23] * [25] = 575 575 congruent to 1 mod 41 [25] is the inverse I have started the other one but I am doing so...
Thursday, 1 November 2018

multivariable calculus - What is the relationship between the functions $f(x,y,z) = x^2+y^2+z^2, z = 1- x - y$, and $g(x,y) = x^2 + y^2 + (1-x-y)^2$

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Suppose I have a function $$f(x,y,z) = x^2+y^2+z^2$$ Obviously, we cannot have a visualization of such function. However, suppose that the f...
Tuesday, 30 October 2018

analysis - Prove that the Union of [1/n,n] = (0,∞) from n=1 to ∞

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So I'm having trouble starting the proof mainly because I don't know which proof technique to use. I thought about using the Princip...

Math induction, how does it work?

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I'm reading a book(concrete Mathematics) and it uses a lot the concept of 'Math induction'. Thought I've been readin...