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1d
comment $G$ a finite group such that $x^2 = e$ for each $x$ implies $G \cong \mathbb{Z}_2 \times … \times \mathbb{Z}_2$ ($n$ factors)
@agha: Note that the solution suggested by egreg is very simple.
1d
comment Suggest an unbiased estimator for θ and provide an estimate for the standard error of your estimator.
The point is to remind you of the meaning of the very important term unbiased estimator.
1d
comment Suggest an unbiased estimator for θ and provide an estimate for the standard error of your estimator.
Yes, Well, we could be silly and use $Y_1$, which would be technically correct but throws away information (it has larger variance than $\bar{Y}$ if $n\gt1$).
1d
comment Suggest an unbiased estimator for θ and provide an estimate for the standard error of your estimator.
The question is answered in the question.
1d
comment Square Free congruence modulo n
You are welcome. I wrote in a condensed way because you asked for hints. Note that to finish, since $p^2$ does not divide $p^n-p$, it follows that $n$ cannot divide $p^n-p$, contradicting the assumption that $n$ divides $a^n-a$ for all $a$.
1d
comment Square Free congruence modulo n
If $n\ge 2$, then $p^2$ divides $p^n$. For example, $p^2$ divides $p^5$. If it also divided $p^n-p$, then, as I wrote above, it would divide $p$. But it doesn't. So $p^2$ cannot divide $p^n-p$. Or using congruences, $p^n-p\equiv -p\not\equiv 0\pmod{p^2}$.
1d
comment Square Free congruence modulo n
As mentioned in the answer, $p^2$ divides $p^n$ (because $n\ge 2$). Suppose $p^2$ divided $p^n-p$. Then $p^2$ would divide $p^2-(p^2-p)=p$. But it does not.
1d
answered Square Free congruence modulo n
1d
answered Expected value problem: flip $6$ fair coins before we obtain $3$ heads and $3$ tails?
1d
comment Smallest $n$ such that $U(n)$ contains a subgroup isomorphic to $\mathbb Z_5 \oplus \mathbb Z_5$
Why use $11^2$ when $11$ works?
1d
comment Show by mathematical induction that the gcd(n,n+1) = 1 for every integer n.
Technically it is. We have proved that $A(k)$ implies $A(k+1)$.
1d
comment If $f:\mathbb{Z} \to \mathbb{Z}$ is an isomorphism, prove that $f$ is the identity map.
If it is a ring isomorphism, one can prove that $f(1)=1$. It then follows, using the argument that you sketched, that $f$ is the identity map.
1d
comment Combinatorics: number of ways to choose $n$ distinct items from k boxes, each containing $s_i$ items?
Sum of all products of $n$ numbers chosen from the $s_i$. This elementary symmetric function can be expressed in various ways in terms of other symmetric functions, but there is no "best" such expression.
1d
comment Suppose {A} is a sequence that assumes only integer values, under what conditions does this sequence converge?
Ultimately constant.
1d
revised Three fair dice are rolled one time. What is the probability of at least one $6$?
added 221 characters in body
1d
answered Three fair dice are rolled one time. What is the probability of at least one $6$?
1d
comment Three fair dice are rolled one time. What is the probability of at least one $6$?
The probability of not $6$ three times in a row is $(5/6)^3$, so the probability of at least one $6$ is $1-(5/6)^3$. This is $\frac{216-125}{216}$. So instead of your $93$ we have $91$.
1d
comment Find the limit of fraction involving logarithms
We can use L'Hospital's Rule once then a bit of algebra.
1d
comment Three fair dice are rolled one time. What is the probability of at least one $6$?
First find the probability of no $6$. The number $10/216$ is not right, much too low.
1d
comment Finding limit via Sandwich Theorem: $\lim_{n\to\infty} n\sum_{n+1}^{2n} \frac{1}{i^2}$
We can estimate the sum using a couple of related integrals.