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answered Are $X$ and $Y$ necessarily normal if the the sum $Z=X+Y$ is normal?
May
11
answered problem of numeric sequence
May
11
comment Sum of order statistics
I would suggest you search Math.SE for this and if you don't find a satisfactory hint/answer, ask a separate question. But yes, there are tactics for those.
May
11
comment Formula for $E(X^4)$ as integral of complementary CDF of random variable $X$
Yes it is. Steps are all correct.
May
11
comment Formula for $E(X^4)$ as integral of complementary CDF of random variable $X$
Another way to understand this is to see that it is same as $E[1_{\{u \leq X\}}] = P[X > u]$
May
11
comment Formula for $E(X^4)$ as integral of complementary CDF of random variable $X$
No. It evaluates to $\int_0^\infty 1_{\{u\leq x\}} dF(x) = \int_u^\infty dF(x) = P[X > u]$
May
11
revised Sum of order statistics
added 345 characters in body
May
11
comment Sum of order statistics
Are you looking for sums of all the ordered statistics or only some of them?
May
11
answered Sum of order statistics
May
11
answered Prove that $ne^{-na} \leq C e^{\frac{-na}{2}}$
May
11
answered Formula for $E(X^4)$ as integral of complementary CDF of random variable $X$
May
8
reviewed Approve Calculate Rotation Matrix to align Vector A to Vector B in 3d?
May
8
reviewed Approve Proving uniqueness of limits
May
3
revised Bound Involving Submartingales
added 552 characters in body
May
3
comment Bound Involving Submartingales
Wait. A key aspect of applying Doob's Inequality here is that $S_n$ is a martingale, which I know is true when $X_i$ are iid mean zero. But here $E[S_n|S_{n-1}] = S_{n-1} + E[X_n |S_{n-1}]$. In iid case $E[X_n |S_{n-1}] = E[X_n] =0$. But we can't conclude this when they are not iid.
May
3
comment Bound Involving Submartingales
Oh. I didn't see that. Give me some time to see if I can fix it. Also could you tell me the source of this problem?
May
3
comment Bound Involving Submartingales
Don't worry about the second part. What happens when you multiply a negative number ($\xi$) on both sides of $\{m_n \leq -\lambda\}$?
May
3
answered Bound Involving Submartingales
May
3
comment What is an “arithmetic progression”?
Did you try googling it?
May
2
comment Must be Bayes' theorem
Then the maid can pick two notes in $\binom{3}{2}$ ways.