Work these problems on a separate sheet of paper. Staple sheets together, in order. Be neat. Always give enough work and clear explanation so that fellow students could follow what you did (from start to finish) just by reading your paper. 1. (See. 3.3) A certain brand of tuperware is available in four different capacities: 8em2, 16cm2, 2tem and 30cm. Let X = the capacity of a piece of tuperware of this brand sold at a certain store. Suppose that X has pmf 16 24 30 P{x) | .1 | .4 | 2 3 (a) Compute E(X), E(x?) and V(X). (b) If the price of a piece of tuperware having capacity X is given by 60X-545, what is the expeeted price paid by the next customer to buy a piece of tuperware? (e) What is the variance of the price paid by the next customer? (d) Suppose that although the capacity of apiece of tuperware is X, the actual capacity is given by X-009X. What is the expected actual capacity of the piece of tuperware purchased by the next customer? 2. (Sec. 3.3) Possible values of X, the number of calculators from a public high school classroom submitted for repair that must be replaced, are 1, 3, 5 and 7. with corresponding probahilities .10,.25, 35 and 30, respectively (a) Calculate E(X) and E(s- X) (b) Would the repair facility make a larger profit if they charged a flat rate of S90 regardless of the number of components needing repair, or if they charged the amount $185/(8-X)? 3. (Sec. 3.3) A Bernoulli random variable X is one which can only take the values 0 or 1. Suppose P(X 1)-p, ie. the probability of "success" is p (a) Find E(X) in terms of p. (b) Find E(X) in terms of p. (e) Verify that V(X) = p(1 -- p). 4. (Sec. 3.4) In 2016, the United States Census Bureau estimates that 1 in 13 children in the United States have a food allergy of some sort. Consider selecting a random sample of 30 children and let X be the number in the sample who have a food allergy. Note that X has a binomial distribution. (a) Determine both P(X < 3) and P(X < 3) (b) Determine P(X 4). (e) Determine P(1X< 4. (d) What is the expected value of X7 What is the standard deviation of X? (e) In a class consisting of 45 children, what is the probability that none of them have a food allergy? Cs Scanned with CamScanner

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Topic Video
Question

If the price of a piece of tuperware having capacity X is given by 60X-545, what is the expected price paid by the next customer to buy a piece of tuperware?

Work these problems on a separate sheet of paper. Staple sheets together, in order. Be neat. Always give
enough work and clear explanation so that fellow students could follow what you did (from
start to finish) just by reading your paper.
1. (See. 3.3) A certain brand of tuperware is available in four different capacities: 8em2, 16cm2, 2tem
and 30cm. Let X = the capacity of a piece of tuperware of this brand sold at a certain store. Suppose
that X has pmf
16 24
30
P{x) | .1 | .4 | 2
3
(a) Compute E(X), E(x?) and V(X).
(b) If the price of a piece of tuperware having capacity X is given by 60X-545, what is the expeeted
price paid by the next customer to buy a piece of tuperware?
(e) What is the variance of the price paid by the next customer?
(d) Suppose that although the capacity of apiece of tuperware is X, the actual capacity is given by
X-009X. What is the expected actual capacity of the piece of tuperware purchased by the
next customer?
2. (Sec. 3.3) Possible values of X, the number of calculators from a public high school classroom submitted
for repair that must be replaced, are 1, 3, 5 and 7. with corresponding probahilities .10,.25, 35 and
30, respectively
(a) Calculate E(X) and E(s- X)
(b) Would the repair facility make a larger profit if they charged a flat rate of S90 regardless of the
number of components needing repair, or if they charged the amount $185/(8-X)?
3. (Sec. 3.3) A Bernoulli random variable X is one which can only take the values 0 or 1. Suppose
P(X 1)-p, ie. the probability of "success" is p
(a) Find E(X) in terms of p.
(b) Find E(X) in terms of p.
(e) Verify that V(X) = p(1 -- p).
4. (Sec. 3.4) In 2016, the United States Census Bureau estimates that 1 in 13 children in the United
States have a food allergy of some sort. Consider selecting a random sample of 30 children and let X
be the number in the sample who have a food allergy. Note that X has a binomial distribution.
(a) Determine both P(X < 3) and P(X < 3)
(b) Determine P(X 4).
(e) Determine P(1X< 4.
(d) What is the expected value of X7 What is the standard deviation of X?
(e) In a class consisting of 45 children, what is the probability that none of them have a food allergy?
Cs Scanned with
CamScanner
Transcribed Image Text:Work these problems on a separate sheet of paper. Staple sheets together, in order. Be neat. Always give enough work and clear explanation so that fellow students could follow what you did (from start to finish) just by reading your paper. 1. (See. 3.3) A certain brand of tuperware is available in four different capacities: 8em2, 16cm2, 2tem and 30cm. Let X = the capacity of a piece of tuperware of this brand sold at a certain store. Suppose that X has pmf 16 24 30 P{x) | .1 | .4 | 2 3 (a) Compute E(X), E(x?) and V(X). (b) If the price of a piece of tuperware having capacity X is given by 60X-545, what is the expeeted price paid by the next customer to buy a piece of tuperware? (e) What is the variance of the price paid by the next customer? (d) Suppose that although the capacity of apiece of tuperware is X, the actual capacity is given by X-009X. What is the expected actual capacity of the piece of tuperware purchased by the next customer? 2. (Sec. 3.3) Possible values of X, the number of calculators from a public high school classroom submitted for repair that must be replaced, are 1, 3, 5 and 7. with corresponding probahilities .10,.25, 35 and 30, respectively (a) Calculate E(X) and E(s- X) (b) Would the repair facility make a larger profit if they charged a flat rate of S90 regardless of the number of components needing repair, or if they charged the amount $185/(8-X)? 3. (Sec. 3.3) A Bernoulli random variable X is one which can only take the values 0 or 1. Suppose P(X 1)-p, ie. the probability of "success" is p (a) Find E(X) in terms of p. (b) Find E(X) in terms of p. (e) Verify that V(X) = p(1 -- p). 4. (Sec. 3.4) In 2016, the United States Census Bureau estimates that 1 in 13 children in the United States have a food allergy of some sort. Consider selecting a random sample of 30 children and let X be the number in the sample who have a food allergy. Note that X has a binomial distribution. (a) Determine both P(X < 3) and P(X < 3) (b) Determine P(X 4). (e) Determine P(1X< 4. (d) What is the expected value of X7 What is the standard deviation of X? (e) In a class consisting of 45 children, what is the probability that none of them have a food allergy? Cs Scanned with CamScanner
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Discrete Probability Distributions
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman