Suppose random variables x and y are independent, and the moment generating function (mgf) of x is m_x = (4/5 e^t + 1/5)^9 and the mgf of y is m_y(t) = exp(3e^t - 3). a) use the mgt derivative approach to find the expectation and variance of x and of y. b) for each of the two variables x and y, based on the form of the respective mgt, determine the marginal distribution of the variable (the name with the value(s) of parameter( and without taking any derivatives find the expectation and variance of the variable. provide details. c) find p(2x + y = 4). d) find p(xy = 0). e) find e(xy).

given hc ∥ gd.¯¯¯¯¯¯which statement is true

step-by-step explanation:

∠cbe and ∠deb are same-side interior angles

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240