Let `x_1,x_2…x_n` be a set of observations with mean value 0 and variance `sigma_x^2`and `y_1,y_2,…,y_m` be another set of observations with mean value 0 and variance… Find the mean value and variance of the set of observations `x_1,x_2,,,,x_n, y_1,y_2,…y_m` combined.

Write the value of x-intercept of the plane x+y+2z=1 .

Find the area enclosed by y^2=x, x=0,y=1

Find the extreme values of y = cos x(1+sin x), x in [0,2pi]

Find the area of the region enclosed by x=1+y^2,X=0,y=3,y=6

Suppose the values x_1, x_2,…..x_n having frequency f_1, f_2…...f_n respectively have mean value overset- x and variation sigma^2 .Let a be a fixed real number. Show that the values x_1+a,x_2+a,….,x_n+a with frequency f_1,f_2….f_n respectively will have mean value overset-x+a and variance sigma

Let X and Y be sets containing m and n elements respectively.What is the total number of functions from X to Y.

Write the value of (dy)/dx at (1,0) where x^2y+y^2+x=0 .