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1d
comment power series expansion of the square root of a Hermitian matrix
@Tarek No, as already explained, this uses the expansion of $\sqrt{1-x}$ at $x=0$ (for $x=I-c^{-1}H$), not the expansion of $\sqrt{x}$ at $x=0$ (which would be what, anyway?). After more than two years, this comment of yours is rather disquieting, I must say...
1d
comment Find $E(X_1X_2 \mid X_2 X_3)$ for i.i.d. symmetric Bernoulli random variables $X_k$
Then use that $X_1$ is independent of $(X_2,X_3)$ hence $E(X_1X_2\mid X_2X_3)=E(X_1)E(X_2\mid X_2X_3)=$ $____$.
1d
revised Find $E(X_1X_2 \mid X_2 X_3)$ for i.i.d. symmetric Bernoulli random variables $X_k$
edited body; edited tags; edited title
1d
comment Find $E(X_1X_2 \mid X_2 X_3)$ for i.i.d. symmetric Bernoulli random variables $X_k$
Did you try to compute the joint distribution of $(X_1X_2,X_2X_3)$? Even brute force yields it readily, since we are talking about a measure on 4 points...
1d
revised Solving Differential Equation $\frac{dy}{dx} = 1 -\sin(x+y)/(\sin y \cos x)$ by separating variables
deleted 19 characters in body
1d
comment Prove sequence ${x_{n + 1}} = \sin {x_n},{x_1} = 1 $ has a limit
Related: math.stackexchange.com/questions/45283
1d
revised Conditional expectation of the maximum of two independent random variables, given one of them
added 33 characters in body; edited tags
1d
comment Conditional expectation of the maximum of two independent random variables, given one of them
The identity follows from the general fact that for every integrable $M$, event $A$ and partition $(B)$, $$E(M\mid A)=\sum_BE(M\mathbf 1_B\mid A)=\sum_BE(M\mathbf 1_B\mathbf 1_A)P(A)^{-1}=\sum_BE(M\mid A,B)P(B\mid A).$$ Apply this to $M=\max(X_1,X_2)$, $A=\{X_2=x\}$ and $(B)$ the partition into the events $\{M=x\}$ and $\{M\ne x\}$ (and forget that one is conditioning on an event of probability zero hence the whole solution should be rewritten using the correct definition of conditional expectation...).
1d
comment power series expansion of the square root of a Hermitian matrix
Got something from the answer below?
2d
revised Evaluating $\int_0^{\pi /2}\left(\frac{1}{\sqrt{\tan(x)}}+\frac{1}{\sqrt{\arctan(x)}}\right) dx$
edited body; edited title
2d
comment Proving $\frac{n^n}{3^n} < n!$ for $n\ge6$ by induction
The reduction to $3>\left(1+\frac1m\right)^{m+1}$ is suboptimal, this inequality fails for some small values of $m$, and the argument using $\left(1+\frac1m\right)^{m+1}>\left(1+\frac1{m+1}\right)^{m+1}$ is squarely wrong. Not sure I am very fond of such a "HINT"...
2d
comment Confused about rules for solving systems of linear equations
@Doc And now that you have been given what you call "the reason", what?
2d
comment What is the distribution of a binomial variable where the number of trials is itself random?
$$P(X=i)=\frac1n\sum_{k=\max(i,1)}^n{k\choose i}\frac1{2^k}$$
2d
comment cauchy sequence in metric space
"I think {x} and {x^2} are not cauchy sequences" True, since these are not sequences at all (but the comment is slightly odd).
2d
comment How can I indicate that n and k are natural numbers in ∀n[(∀k < n P(k)) → P(n)].
$$P(1)\land P(2)\land P(3)$$
2d
comment Prove the equation has unique class of solutions
@user109899 Theoretically true, but this automatic reaction/admonestation seems spectacularly ill-adapted to the character at hand.
2d
revised What is wrong with this logic based on a geometric distribution?
added 276 characters in body
2d
comment What is the integer part of $\sum_{i=2}^{9999} \frac {1}{\sqrt i}?$
"No" to what? @DanielFischer's question is to know what you know.
2d
comment Jensen's inequality problem
One wonders which cases you looked at before asking since (nearly) every example works.
2d
comment Neccesary condition for perpendicularity
Why? $ $ $ $ $ $