If (X, Y) has the normal distribution in two dimensions with zero means and unit variances and correlation coefficient \rho, then to prove that the expectation of the greater of X and Y is \sqrt{(1-\rho)\pi}.
How to proceed with it? Help please.
I have to solve the integral equation y(x)= -1+\int_0^x(y(t)-sin(t))dt by the method of successive approximation taking y_0(x)=-1.
Sol: After simplification the given equation we have
y(x)=-2+cos(x)+\int_0^x y(t)dt . So comparing it with y(x)=f(x)+\lambda\int_0^x k(x,t)y(t))dt we have...
I have to solve the integral equation y(x)=1+2\int_0^x(t+y(t))dt by the method of successive approximation taking y_0(x)=1.
Sol: After simplification the given equation we have
y(x)=1+x^2+2\int_0^xy(t)dt. So comparing it with y(x)=f(x)+\lambda\int_0^x k(x,t)y(t))dt we have
f(x)=1+x^2...
How to show in details that the function |x| satisfies Dirichlet's conditions on [-\pi \pi].;
I know the Dirichlet's conditions, but facing problems to apply it on the given function.
If ( X,Y ) has the normal distributions in two dimensions with zero means and unit variances and the correlation coefficient r, then how to prove that the expectation of the greater of X and Y is \sqrt{(1-r)\pi}?
Find the Fourier cosine series of cos(x) from x=0 ~to ~\pi
Here the Fourier series is given by
f(x)=\frac{1}{2}a_0+\sum_{n=1}^{\inf}a_n cos nx dx where a_n=\frac{2}{\pi}\int_0^\pi f(x)cos nx dx
I am facing problem to solve it. I am getting a_0=0 and a_n=0 so the Fourier series becomes...
Q.
In order to estimate the total weight of rice of 100 bags, a sample of 25 bags was weighted, giving the average weight of 50 kg. If the population standard deviation is 1.5kg, estimate the total weight of 100 bags and find the standard error of the estimate. Sol:
Here sample mean is 50. So...
Using second mean value theorem in Bonnet's form show that there exists a
p in [a,b] such that
\int_a^b e^{-x}cos x dx =sin ~p
I know the theorem but how to show this using that theorem .