Ted is not particularly creative. he uses the pickup line "if i could rearrange the alphabet, i'd put u and i together." the random variable x is the number of women ted approaches before encountering one who reacts positively. determine whether a probability distribution is given. if a probability distribution is given, find its mean and standard deviation. if a probability distribution is not given, identify the requirements that are not satisfied.
x
p(x)

0
0.001
1
0.007
2
0.033
3
0.059
does the table show a probability distribution? select all that apply.

It is not  a probability  distribution as some data is missing.

Step-by-step explanation:

It is not  a probability  distribution as some data is missing.

Since it  is discrete and,

P(X = x)

= (0.001 + 0.007 + 0.033 + 0.059)

= 0.1 ≠ 1

and we know that for

to be classified as a discrete probability function,

1. 0 ≤ P(X = x) ≤ 1  and   ∀ x ∈ R and

2. P(X = x) = 1

where M is  the support of X or the set of points where P(X = x) > 0

must hold.

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.