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

18.75 gallons

step-by-step explanation:

the degrees would remain the same ( the number to the left of the decimal point.

the multiply the decimal by 60 to get the minutes and use the numbers to the left of the decimal point.

then multiply the decimal portion of that by 60 for the seconds and round off as needed.

39 .956652

the 39 remains the degrees.

the minutes = 0.956652 x 60 = 57.39912

the minutes = 57

the seconds = 0.39912 x 60 = 23.95 = 24 ( rounded to nearest tenth)

so 39.956652 = 39 degrees, 57 minutes and 24 seconds

-75.159809

the -75 remains the degrees

the minutes = 0.159809 x 60 = 9.58854

the minutes = 9

the seconds = 0.58854 x 60 = 35.31, rounded to nearest tenth = 35.3 seconds

so -75.159809 = -75 degrees, 9 minutes and 35.3 seconds.

the first coordinate is north or south, since it it positive it is north.

the second number is east or west, because it is negative it is west.

39 degrees, 57 minutes and 24 seconds n

-75 degrees, 9 minutes and 35.3 seconds w

find the vertical and horizontal asymptotes of the function f x = 5 x − 1 . to find the vertical asymptote, equate the denominator to zero and solve for . since the degree of the polynomial in the numerator is less than that of the denominator, the horizontal asymptote is .

step-by-step explanation:

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