Based on long years of experience, an instructor in the principles of economics has determined that in her class the probability distribution of X, the number of students absent on Mondays, is as follows:

col1 X: 0 1 2 3 4 5 6 7
col2 F(x)0.005 0.025 0.310 0.340 0.220 0.080 0.019 0.001

(a) Sketch a probability function of X
(b) Find the probability that on a given Monday either two or three or four students will be absent
(c) Find the probability that on a given Monday more than three students are absent
(d) Compute the expected value of the random variable X. Interpret this expected value.
(e) Compute the variance and standard deviation of the random variable X
(f) Compute the expected value and variance of Y=7X+3

900 degrees

step-by-step explanation:

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

answer: it's d

step-by-step explanation: