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).

7 ft 6 in means 7 1/2, because 6 in is 1/2 of a foot. 7 ft 8 in means 7 2/3 because 8 in is 2/3 of a foot. 23/3 = 7 2/3. 15/2 = 7 1/2.

23/3   *   15/2   = 57 1/2

step-by-step explanation:

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204

the answer is c: divide the arc's degree measure by 360°, then multiply by the circumference of the circle.