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16h
comment Recalculate Standard Deviation
Correct. If you knew the number of samples you could compute $\sum_k x_k $ and $\sum_k x_k^2$, but without that you are missing some constraint...
16h
comment Recalculate Standard Deviation
Then you can't do it. If there were a huge number of samples, one more would have little impact where as if there were just two samples, the impact would be more significant.
16h
comment Recalculate Standard Deviation
Do you know how many samples you have?
16h
comment Recalculate Standard Deviation
In general, adding a different value will change the mean and the variance. I don't understand how you concluded that adding the above value won't affect the variance?
19h
comment distance on a normed space
@user308560: Yes, it looks correct. In general, for these sorts of things, since $d_Y$ is defined in terms of $\|\cdot\|$, I think is is easier to work from the corresponding relation for $\|\cdot\|$ and then use that to get the relation for $N$.
19h
comment distance on a normed space
If $y_k$ is a sequence in $Y$ such that $ \|a-y_k\| \to N(\bar{a})$ then $y'_k=(b-a)+y_k$ is a sequence in $Y$ such that $\|b-y'_k \| = \|a-y_k\| \to N(\bar{a})$, from which it follows that $N(\bar{b}) \le N(\bar{a})$. Switching the roles of $a,b$ gives the desired result.
19h
comment how to determine a matrix has a single eigenvalue
@MooS: The OP mentioned nothing about computation effort. It is trivial to verify that $A^4 = (A^2)^2 = 0$ (which is tantamount to what you have done in your answer) from which it follows that (i) the characteristic polynomial is $x \mapsto x^4$ and (ii) all eigenvalues are zero. This sort of pettiness is why my interest in helping out at MSE has significantly waned.
1d
comment distance on a normed space
Glad to help! ${}{}$
1d
comment how to determine a matrix has a single eigenvalue
Why the downvote? Really, please tell me.
1d
comment distance on a normed space
Your solution is correct, but I prefer proofs that follow directly from the relevant inequality directly.
1d
comment Proving that a set infers a norm given certain conditions
If $\lambda \neq 0 $ then $x \in \lambda \bar{B}$ iff there is some $y \in \bar{B}$ such that $x=\lambda y$ iff there is some $y$ such that $y = {1 \over \lambda } x \in \bar{B}$.
1d
comment How do you calculate the change in thickness of a cylinder, if you shave off a flat section?
@Giffyguy: Don't think negatively like that. Lots of problems become simple where we can separate the clutter from the essentials. Sometimes its hard to distinguish.
2d
comment Prove this integral is analytic
What are the bounds of integration?
Feb
4
comment Compute $(\sin4^\circ)^2 +(\sin8^\circ)^2+(\sin12^\circ)^2+\cdots+(\sin176^\circ)^2$
@ArchisWelankar: It can't be negative, it is the sum of non negative numbers (squares).
Feb
4
comment Is this system Causal?
If $t<0$ then the integral must be zero by the usual way people define the integral of an impulse. Remember, if $t<0$ then $\tau \le t < 0$ as well. I'm going to sleep now, good luck!
Feb
4
comment Is this system Causal?
Yes, just follow exactly the same steps above. If the upper bound was $>t$ then you might have an issue.
Feb
4
comment Is this system Causal?
I don't understand your question.
Feb
4
comment How to calculate the values of a version of a conditional expectation
To illustrate, if $ p \{b\} = 0$, then we can take $E[X |{\cal F_1}] = 0$.
Feb
4
comment How to calculate the values of a version of a conditional expectation
It doesn't matter as long as the value is the same for $b,c$, since it gets 'divided out'.
Feb
4
comment How to calculate the values of a version of a conditional expectation
I think you need to know $p \{b\}, p \{c\}$ to finish the computation. I think that your example assumes $p\{b\} = p \{c\}$.