Recent content by Barioth

Thanks, very clean!

Hi, I'm trying to show that Givien a probability triplet $$(\theta,F,P)$$ with $$G\in F$$ a sub sigma algebra $$E(E(X|G))=E(X)$$ Now I want to use $$E(I_hE(X|G))=E(I_hX)$$ for every $$h\in G $$ since that's pretty much all I've for the definition of conditional expected value. I know this...

I don't have a lot of time, but I'll try to answer Q4. let h=goy :x-->z say $$h(a)=h(b) ==> goy(a)=goy(b)$$ Since y is a bijection we have that y(a)=y(b) if and only if a=b. Say a is not equal to b... then $$y(a)=c$$ and $$ y(b) = d$$ then we have $$g(d) = g(c)$$ Now since d is not equal to...

Hi everyone! I'm kind of lost lately... I finish my undergrad in Pure mathematic last semester. I got accepted for master in mathematic. But I don't know what field to choose.. I'm afraid I won't be getting any job after (and sadly with my student loan, I kind of need a job hehe). I was...

Let $$f(x,y)= \frac{x^3+y^3}{x^2-y} $$if $$x^2 $$is not equal to y and 0 otherwise. I need to find the limit when (x,y)->(0,0) I'm sure the limit exist and is equal to 0, I was unable to conclude switching to polar coordinate so I wana use "the squeeze law" I only have to evaluate $$f(x,y)=...

tacking y=m*x we end up with $$\frac{-2*m*x^4}{(m^2+1)^2*x^4}= \frac{-2*m}{(m²+1)²}$$ This telling me that the limite when (x,y)->(0,0) isn't contiunous. There for the partial derivative doesn't exist at 0. I can conclude that f(x,y) has no derivative at (0,0). Thank you for the help!

Hi, I'm having trouble évaluation the differentiability at (0,0) of the function $$f(x,y)=\frac{x^3}{x^2+y^2}$$ for (x,y) not nul, and $$f(x,y)=0$$ if (x,y)=0 I know f is differentiable if (x,y) isn't nul since the partial derivative are continuous, but I don't know how to evaluate it at...

Hi here is the problem I'm working on, Let $A(x_1)$ be a well formed formula of a language $L$ in which $x_1$ is free, let $a_1$ an invidual constant of $L$, Show that the formula $A(a_1)\rightarrow(\exists x_1)A(x_1)$ is a theorem of $K_L$ on this link, the first slide as the axiom of $K_L$...

The answer to A- 44%, B- 22%, C- 41.5% I don't think these answer on their own will help you... as I said earlier, can you find out the value of...

Don't be, you're giving me some of your free time, I can only thanks you! As for the scope of $\forall x_1$ from it should only be on $A^3_1(...)$ So doing the substition: $$A[t/x]:= (\forall x_1) A^3_1(f^2_1(x_1,x_2),x_2,f^1_1(x_2))\rightarrow (\forall x_2)A^2_1(t,x_3)$$ and then since the...

I'll give you the general formula, Try and see if you can how you can use them. we'll put A: The patient has high blood preasure B: The patient has heart problem From what you have writen Can you write down $P(A), P(B), P(A \cap B)$ Here are some general formula: $P(A \cup B) =...

Tacking for granted that SD stand for standard deviation, since you only have a sample there is no way for you to evaluate the SD/variance of the whole population. Therefore you solve the SD/variance for the sample only.

1) Thanks for tacking the time to write such a complete answer. 2) $$(\forall x_1) A^3_1(f^2_1(x_1,x_2),x_2,f^1_1(x_2))\rightarrow (\forall x_2)A^2_1(x_1,x_3)$$ Would became, following your advisor's convention: $$(\forall x_1) A^3_1[f^2_1[x_1,x_2],x_2,f^1_1[x_2]]\rightarrow (\forall...

I would guess that $$V= X - Y$$ and that you should find the find the marginal distributions of U and [FONT=MathJax_Math]V. You should use the Corollary to find their distribution, then try and apply the marginal distribution stuff. But I could be wrong, good luck!

Hi, The definitions given by the book is: Let A be any wf (well formed formula) of L (the formal system of statement calculus). A term t is "free" for xi (a variable) in A if xi does not occur free in A within the scope of $$\forall$$ xi, where xi is any variable occurring in t. Yeah I...