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Mathematics
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TJT
  • Member for 9 months
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  • London
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19
Roll a dice infinitely many times, what is the probability of getting a 5 before a 6
Dec 19, 2023
2
Verifying my understanding of sigma algebra generated by multiple random variables
Dec 25, 2023
2
Let $(\Omega , {\mathcal A}, P)$, with random variable $X$ and another function $Y:\Omega \rightarrow R$, does $P(X=Y)=1$ guarantee Y to be a R.V?
Jan 6
1
Let $(\Omega,F)$ be a measurable space, $F=\{\varnothing,\Omega\}$, prove that $X:\Omega\to\Bbb R$ is a random variable iff $X$ is constant.
Nov 28, 2023
1
Writing out proof for $E[X|\mathcal{F}] = X$ for X being measurable w.r.p.t sigma algebra $\mathcal{F}$
Dec 10, 2023
1
Find the range of $a$ such that the result of the integration converges
Dec 15, 2023
1
Why $E[X^a] < \infty$ for $a<1$ when $P(X=k) = (k(k+1))^{-1}$ for $k \in N$
Dec 31, 2023
1
Let X and Y be random variables that $X,: \Omega \rightarrow R$ let $g$ be a measurable function that $Y=g(X)$, show $\sigma (Y) \subseteq \sigma (X)$
Jan 1
1
why $(\pi ,4] \in \sigma ({\mathcal C})$? given ${\mathcal C}:=\big \{(a,b]:\, a,b\in {\mathbb Q}\cap [0,10]\big \}, \Omega :=[0,10]$
Jan 5
1
Geometric Brownian motion with volatility as function of time
Jan 17
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5
What's the grammar used in "just what quarter he did not now remember" from the book 1984?