Suppose that h is the probability density function of a continuous random variable.
Let the joint probability density function of X, Y, and Z be
f(x,y,z) = h(x)h(y)h(z) , x,y,zER
Prove that P(X<Y<Z)=1/6
I don't know how to do this at all. This is suppose to be review since this is a...
I have tried to do this, but I am stuck and cannot get them to equal each other.
For f(x)=(1+(-4x))^(-1/2)
The taylor series about 0 is:
sum (-1/2 choose n) (-4x)^n
expanding binomial coefficients:
sum -1/2(-1/2-1)(-1/2-2)...(-1/2-n+1) / n! x (-4)^n (x)^n
sum -1/2(-3/2)(-5/2)...(1/2-n)/n! x...
Deduce that the Taylor series about 0 of 1/sqrt(1-4x) is the series summation (2n choose n) x^n.
From this conclude that summation (2n choose n) x^n converges to 1/sqrt(1-4x) for x in (-1/4,1/4).
Then show that summation (2n choose n) (-1/4)^n = 1/sqrt(1-4(-1/4)) = 1/sqrt(2)
What I know...
the primal problem was:
min (x^T)Px
i found g(r) and the partial derivative of g(r) w.r.t. x to be: x=-1/2(P^-1)(A^T)r
i have found the dual problem to be:
max -1/4(r^T)A(P^(-1))(A^T)r - (b^T)r
subject to r>= 0
I am told to find x* and r* (which i think is just x and r):
i have not...
I am looking for radius of convergence of this power series:
\sum^{\infty}_{n=1}a_{n}x^{n}, where a_{n} is given below.
a_{n} = (n!)^2/(2n)!
I am looking for the lim sup of |a_n| and i am having trouble simplifying it. I know the radius of convergence is suppose to be 4, so the lim sup...
Suppose that the real matrices A and B are orthogonally diagonalizable and AB=BA. Show that AB is orthogonally diagonalizable.
I know that orthogonally diagonalizable means that you can find an orthogonal matrix Q and a Diagonal matrix D so Q^TAQ=D, A=QDQ^T.
I am aware of the Real Spectral...
ok, so i can get 1/px^p for the x>0 case.
but for the x<0 case:
i am struggling
i have,
integ( (-x)^(p-2) x dx)
can i write this as:
= integ( (-1)^p (x)^(p-2) x dx )
so,
= (-1)^p integ (x^(p-2) x dx)
which is just
= (-1)^p 1/p x^p
now how can i put the two together... to make x into |x|?
can you tell me how to integrate this? or at least start, so i can get 1/p|x|^p , i need this small part for a bigger problem and this is making me stuck.
i have thought about what you said about the piecewise, but that confuses me even more as i have to deal with not one but 2 functions now
ok, should i be working from the gradient f(x) -> f(x) or vice versa.
as well , i am getting confused.
is this correct: to work from gradient f(x) -> f(x) we integrate. and f(x)-> gradient f(x) we differentiate.
working from f(x) -> gradient.. i dont see how i can get gradient f(x).
and going...
yes, i have the gradient f(x)= |x|^p-2 x, and i need to find f(x), in class, the definition of gradient is just the derivative w.r.t x of f(x)
so i am asking why 1/p |x|^p is the answer because i don't see how you can use this, to find the gradient function |x|^p-2 x. so I thought the function...
the gradient function is |x|^p-2 x
and i need to find the function, which apparantly is 1/p |x|^p but i can't figure out how to show this.
This is for a bigger problem where the function must be convex. and also p>1
I tried, finding the derivative of 1/p |x|^p , but i don't get the gradient...