## $A$ and $B$ throw a die. Find the probability that the sum of their throws is $6$ February 12    2

The answer comes up as $\frac6{36}$, but I get $\frac5{36}$. The solution lists as possibilites: $$\{(1,5), (2,4),(3,3),(3,3),(4,2),(5,1)\}$$I've always seen this answer as $\frac5{36}$ using a table.This is something that used to confuse me as well.

I have a random process $\phi_t$ which evolves according to the SDE $$d \phi_t = \mu dt+ \sigma \sin \phi_t \,dW_t$$ with $\mu$ and $\sigma$ constants and $W_t$ a Wiener process. The initial condition is $\phi_0 =0$. I would like to know $$\langle \s ## Solving polynomial equation modulo p^n February 12 1 I have to solve the equation$$ X^4 - 3 X^2 + 27 \equiv 0 \bmod 5^k$$for the first few k = 1, \ldots, 6I don't even know how to start, ok, for k=1$$ X^4 - 3 X^2 + 27 \equiv 0 \bmod 5\, ,$$I can guess an answer, like X \equiv 4 \bmod{5}, but ## A proof I'm not sure of: Let n,m be coprime so that xm, yn. Prove (x,y)=1 February 12 2 Let n,m be coprime so that x|m, y|n, x,y \in \mathbb Z. Prove (x,y)=1This proof was shown in class, and I'm not certain of the last step:x|m, y|n so there are a,b \in \mathbb Z so that m=ax and n=by.We know (m,n)=1 so there are You Might Also Like • Assume there is a probability p the have a head when we tossing a coin. Now we would keep on tossing the c ... • Given a labeling of the set of partitions of n with k\leq n parts (numbering choose(n,k)), and compari ... • I would like to know what is the difference between the Matlab optimization toolbox and CVX solver which is ... • Sorry about the title, but I couldn't really figure out how to describe my problem in one sentence... I'm ha ... • I'm struggling a bit with solving a limit problem using L'Hopital's Rule:$$\lim_{x\to\infty} \left(1+\frac{1 ...
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