A study of a large number of towns with approximately 100,000 people estimates the probability that one will have a certain number X of pita restaurants. None of the towns had more than 5. They construct a table of the probability distribution function p(x) = P(X = x) and the cumulative distribution function F(x) = P(X ≤ x) for the number of pita restaurants in a town.
A student shows you a paper copy of these results. Unfortunately, he was caught in a snow shower crossing campus, and only part of the table is readable:

0 1 2 3 4 5
p(x) .20 .14
F(x) .33 .71 .94

(a) Fill in the damaged parts of the table. What is P(1 (b) Calculate the expected number of knots in a beam, E(X).
(c) Write down the probability generating function, πₓ(q) = E(qˣ).
Use it to answer the following question: if 94% of all pita restaurants do takeout, what is the probability that all the pita restaurants in a given town do takeout? (Assume they do not consult each other.)

unless you made a typo, the answers are both a and c.

step-by-step explanation:

1.5/3 is .5 whereas 3/9 is .3333333 not proportional

22/33 is .66666 and 4/6 is also .66666 proportional

2/4 is .5 whereas 142/213 is .66666 not proportional

14/7 is 2 and 7/3.5 is also 2 proportional

you could've also checked it by doing this simple division:

if the larger fraction divides with the smaller fraction to equal 1, it is proportional. so let me show you what i mean:

when i divide 22/33 by 4/6 i get 1, so we know it is proportional, and it is the same with 14/7 and 7/3.5. now if i divide 3/9 by 1.5/3 i get .66666 so therefore we know it is not proportional.

there are many ways to do this so i wanted to show you some possible ways.

d.) 48 units

step-by-step explanation:

(a) x intercepts: -6 and 2

you can obtain these by solving the equation 0=x^2 +4x-12 using your favorite quadratic formula. but it is easy to verify -6 and 2 indeed satisfy this equation.

(b) y intercept: -12

this is obtained by setting x=0: 0^2+4*0-12 = -12

(c) the minimum value is: -16 (this is the vertex)

you can get the vertex by rewriting the equation into the form:

there is no global or local maximum as the function goes to infinity, so only in the limit sense: +infinity.