Hi mfb thanks for the reply. Wouldn't I need the bounds for when I write my final answer as a probability density?
And for the second question, would I sketch x+y=a alongside my fx(x) and fy(y)? So that way as a=x+y has different values I could see how x and y vary? Like I found this...
Hello all,
I am currently working on studying for my P actuary exam and had some questions regarding using convolution for the continuous case of the sum of two independent random variables. I have no problem with the actual integration, but what is troubling me is finding the bounds...
So this is strange...
I looked up a copy of the book online, and the proof was entirely different than the copy I have. Something else to note, sometimes in my book when referring to previous propositions or theorems, rather than saying something like "By Theorem 25" it says "By Theorem (??)"...
\int_{x\in A, f(x)\geq c} f \leq \frac{1}{c} \int_{E} f
Thanks for this !
Yes the m(A) < δ and it is saying that if you integrate over this set A (a measurable subset of E), that the value of the integral will be < ε
What happened was I split the domain of A into two parts, one where f(x) < c and one where f(x) >= c
Then I applied Chebychev's inequality to the part where f(x) >= c but I was confused as to why
\int\limits_{x in A s.t. f(x)>=c} \ <= (1/c) * \int\limits_E \
edit: don't think that...
Hello all,
I am currently working through a proof in my Real Analysis book, by Royden/Fitzpatrick and I'm confused on a part.
if f is a measurable function on E, f is integrable over E, and A is a measurable subset of E with measure less than δ, then ∫|f| < ε...
hmm I have never used polar coordinates with an epsilon delta proof before
so x=rcosθ
and y=rsin
so f(x,y) is rcosθ(cos^{2}θ - sin^{2}θ)
and r<\delta and cosθ <= 1
so f(x,y) < \delta(cos^{2}θ - sin^{2}θ)
which = \deltacos(2θ) <= \delta(1) = \delta
set \delta = \epsilon...
Homework Statement
Prove:
f(x,y) = \frac{x(x^{2}-y^{2}}{(x^{2}+y^{2}} if (x,y) \neq (0,0)
0 if (x,y) = (0,0)
is continuous at the origin
Homework Equations
\forall \epsilon > 0 \exists \delta > 0 s.t. if |(x,y)| < \delta then |f(x,y)| < \epsilon
(Since we are proving...
Homework Statement
Going at top speed, grand prix driver X leads archrival Y by
a steady 3 miles. Only 2 miles from the nish, X runs out of gas. Thereafter, X decelerates with
time at a rate proportional to the square of her (instantaneous) speed and in the next mile X's speed
exactly...
do you have any idea of what the dimension of M2x3(F) is?
Since it is 2x3, the dimension would be 6?
Because we would need 6 vectors:
\begin{array}{ccc}
1 & 0 & 0 \\
0 & 0 & 0 \end{array},
\begin{array}{ccc}
0 & 0 & 0 \\
1 & 0 & 0 \end{array},
\begin{array}{ccc}
0 &...
Homework Statement
Prove T is a linear transformation and find bases for both N(T) and R(T).
Homework Equations
The Attempt at a Solution
T:M2x3(F) \rightarrow M2x2(F) defined by:
T(a11 a12 a13)
(a21 a22 a23)
(this is one matrix)
=
(2a11-a12 a13+2a12)...