Suppose that x and y are zero-mean jointly gaussian random variables with variances and , respectively, and correlation coefficient . the joint pdf surface is a flattened bell. now, suppose we rotate the coordinate axes by an angle . the random point in the plane whose coordinates are (x, y) with respect to the old axes now has coordinates (z, w) with respect to the new axes where , and . the joint pdf surface is still the same shape as before, but since the coordinate axes have been changed, the pdf surface is defined by a different formula.
(a)find the means and variances of the random variables z and w, and compute . from these values, write the new formula for the joint pdf surface.
(b)for suitable choice(s) of , the new coordinate axes are parallel to the major and minor axes of the ellipses that are the contours of the joint pdf surface. for these choices of , z and ware independent gaussian random variables. find all angles such that z and w are independent gaussian

2 equivalent expressions to represent the area of a rectangle and the top is n-3 and the side is 2

area of the rectangle = length * width

given length = n - 3

width = 2

replace it in the area

so area of the rectangle = (n-3) *2

= 2(n-3)

one of the expression is 2(n-3)

to get another expression we distribute 2 inside the parenthesis

2(n-3) is 2n - 6

so another expression is 2n - 6

two equivalent expression are

2(n - 3)   , 2n - 6

c.

step-by-step explanation:

sorry for any inconvenience this may have caused try again

try again.

(a) x intercepts: -6 and 2

you can obtain these by solving the equation 0=x^2 +4x-12 using your favorite quadratic formula. but it is easy to verify -6 and 2 indeed satisfy this equation.

(b) y intercept: -12

this is obtained by setting x=0: 0^2+4*0-12 = -12

(c) the minimum value is: -16 (this is the vertex)

you can get the vertex by rewriting the equation into the form:

there is no global or local maximum as the function goes to infinity, so only in the limit sense: +infinity.