Recent content by Suvadip

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.

if , then what will be . In fact I was solving the integral equation by the method of successive approximation.

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 $$y(x)=f(x)+\lambda\int_0^x k(x,t)y(t))dt$$...

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...

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 $$\sqrt{(1-r)\pi}$$?

Ohh sorry, $$a_n=1~ for ~n=1, a_n=0$$ otherwise Then Fourier cosine series for cosx is cosx?

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...

Find the least positive integer x such that x=5 (mod 7), x=7 (mod 11) and x=3(mod 13). How to proceed?

Show that 2x^3+x^2+3x-1 = 0 (mod 5) has exactly three solutionsHow to proceed with it?

$$F$$ is the distribution function.

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 .

Given that $$r1=2a-3b+c$$ $$r2=3a-5b+2c$$ $$r3=4a-5b+c$$ where $$a, b, c$$ are non-zero and non coplannar vectors How to prove that $$r1, r2 , r3$$ are linearly dependent? I have moved with $$c1*r1+c2*r2+c3*r3=0$$ but confused how to show that at leat one of $$c1, c2, c3$$ is non-zero. We...

I have to prove $$x^8+1= P_0^3(x^2-2xcos\frac{(2k+1)\pi}{8}+1)$$ where $$P_0^3$$ means product from $$k=0$$ to $$k=3$$.I tried it but got $$x^8+1= P_0^3(x^2-a_k^2)$$ where $$a_k=cos\frac{(2k+1)\pi}{8}+isin\frac{(2k+1)\pi}{8}$$. How to arrive at the correct answer

Upto that I have already done. I have confusion about how to find $$F(x)$$