# André Nicolas

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 45s comment If a certain random variable has P(x <= 500) = .5 and p(x > 650) = .0227. Find $\sigma_x$ Chances are that for absolutely no good reason you are expected to assume the random variable is normally distributed! 8m answered prove for p(x) which is a quadratic polynomial 15m answered Sequence with partial limits (0,1] 25m comment Proof expectation of bernoulli distribution Because it works! If you are interested in the sum $\sum ka_k x^{k-1}$, and you have a closed form for $\sum a_x^k$, say $f(x)$, then the sum you are interested in is $f'(x)$. If you are interested in $\sum \frac{a_k}{k+1}x^{k+1}$, you can similarly integrate $f(x)$. These are two important manipulations on generating functions. There are other ways to tackle your particular sum. 42m comment Solving for a and b Quadratic Formula sounds good. Treat separately the case $a=0$. 47m answered Proof expectation of bernoulli distribution 1h answered probability x is odd in a geometric distribution 1h comment Are there infinite positive $n \in \Bbb N$ such that ($D^+_n$, |) is isomorphic to ($D^+_{4100}$, |)? Let $m=p_1^{a_1}\cdots p_k^{a_k}$ and $n=q_1^{a_1}\cdots q_k^{a_k}$ where the $p_i$ are distinct primes and the $q_i$ are distinct primes. Then the prime power decompositions have the same structure. (The number of primes is the same, and the sequence of exponents is the same.) So for example $2^2\cdot 3^7$ has the same structure as $11^2\cdot 2^7$. 1h comment Separable Differential Equations For the first, rewrite as $y\,dy=\frac{t}{1+t^2}\,dt$. Integrate. 2h answered Finding the roots of the sum of complex numbers 2h comment A question about uncountable set with infinite subsets of natural numbers. Call a subset $A$ bad if $A$ is finite or its complement is finite. How many bad $A$ are there? 2h comment Are there infinite positive $n \in \Bbb N$ such that ($D^+_n$, |) is isomorphic to ($D^+_{4100}$, |)? For any two numbers $m$ and $n$, we get isomorphism if the prime power decompositions of $m$ and $n$ have the same structure. The actual primes used do not matter. 2h comment Are there infinite positive $n \in \Bbb N$ such that ($D^+_n$, |) is isomorphic to ($D^+_{4100}$, |)? The count of the number of divisors is not enough to prove isomorphism. Note that for example $3^{17}$ also has $18$ (positive) divisors. But for the $n$ of the hint, we get an isomorphism by mapping any divisor $2^a5^b 41^c$ of $4100$ to the divisor $p^aq^b r^c$ of $n$. This mapping preserves the divisibility relation. 2h answered Are there infinite positive $n \in \Bbb N$ such that ($D^+_n$, |) is isomorphic to ($D^+_{4100}$, |)? 2h answered I don't understand this solution at all 3h comment Probability of life expectancy That is correct. And $\Pr(B\cap A)=\Pr(B)$, so we get $\frac{1/2}{4/5}$. 3h answered Expected number of bridges 3h comment Multiple Poisson Distributions Question Thanks for picking it up, I had a typo. 3h revised Multiple Poisson Distributions Question deleted 12 characters in body 3h answered Multiple Poisson Distributions Question