In an annual poll about consumption habits, telephone interviews were conducted for a random sample of 1,014 adults aged 18 and over. One of the questions was, "How many cups of coffee, if any, do you drink on an average day?" The following table shows the results obtained.Number ofCups per DayNumber ofResponses0365126421933914 or more101Define a random variable x = number of cups of coffee consumed on an average day. Let x = 4 represent four or more cups.(a)Develop a probability distribution for x. (Round your answers to three decimal places.)Number ofCups per Dayf(x)0 1 2 3 4 or more (b)Compute the expected value of x. (Round your answer to three decimal places.)E(x) = (c)Compute the variance of x. (Round your answer to three decimal places.)Var(x) = (d)Suppose we are only interested in adults who drink at least one cup of coffee on an average day. For this group, let y = the number of cups of coffee consumed on an average day. Compute the expected value of y. (Round your answer to three decimal places.)E(y) = Compare the expected value of y to the expected value of x.When we only take into account adults that drink at least one cup of coffee per day, the expected value is the expected value of x

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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In an annual poll about consumption habits, telephone interviews were conducted for a random sample of 1,014 adults aged 18 and over. One of the questions was, "How many cups of coffee, if any, do you drink on an average day?" The following table shows the results obtained.

Number of Cups per Day	Number of Responses
0	365
1	264
2	193
3	91
4 or more	101

Define a random variable x = number of cups of coffee consumed on an average day. Let

x = 4

represent four or more cups.

(a)

Develop a probability distribution for x. (Round your answers to three decimal places.)

Number of Cups per Day	f(x)
0
1
2
3
4 or more

(b)

Compute the expected value of x. (Round your answer to three decimal places.)

E(x) =

(c)

Compute the variance of x. (Round your answer to three decimal places.)

Var(x) =

(d)

Suppose we are only interested in adults who drink at least one cup of coffee on an average day. For this group, let y = the number of cups of coffee consumed on an average day. Compute the expected value of y. (Round your answer to three decimal places.)

E(y) =

Compare the expected value of y to the expected value of x.

When we only take into account adults that drink at least one cup of coffee per day, the expected value is the expected value of x

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