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Chapter 4: Q.12 (page 282)

We know that for a probability distribution function to be discrete, it must have two characteristics. One is that the sum of the probabilities is one. What is the other characteristic?

Use the following information to answer the next five exercises: Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35%of the time, four events 25%of the time, three events 20%of the time, two events 10%of the time, one event 5%of the time, and no events 5% of the time.

Short Answer

Expert verified

Each random variable Xhas a probability greater than or equal to zero.

Step by step solution

01

Given Information

Sam practices music three times a week. She exercises on a regular basis. 85%of the time for all three days, 8%of the time for two days, 4%of the time for one day, and 3%of the time for no days.

02

Concept Used

A random variable depicts the problem's characteristics and allows us to make decisions. X is the number of days in a week that Ellen has music practice. P(X)is stated to be the probability mass function of a discrete variable X only when, according to the assumptions of discrete distribution,

鈭�P(X)=1

03

Calculation

Another feature of discrete random variables is that they are

P(X)鈮�0for allX

04

Conclusion

The feature of a random variable is that it is randomly distributed is

P(X)鈮�0for allX

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Most popular questions from this chapter

At The Fencing Center, 60% of the fencers use the foil as their main weapon. We randomly survey 25 fencers at The Fencing Center. We are interested in the number of fencers who do not use the foil as their main weapon.

a. In words, define the random variable X.

b. List the values that X may take on.

c. Give the distribution of X. X ~ _____(_____,_____)

d. How many are expected to not to use the foil as their main weapon?

e. Find the probability that six do not use the foil as their main weapon.

f. Based on numerical values, would you be surprised if all 25 did not use foil as their main weapon? Justify your answer numerically.

On average, how many batches should the baker make?

Use the following information to answer the next four exercises: Ellen has music practice three days a week. She practices

for all of the three days 85% of the time, two days 8% of the time, one day 4% of the time, and no days 3%of the time. One

week is selected at random.

Suppose that the PDF for the number of years it takes to earn a Bachelor of Science (B.S.) degree is given in Table 4.31.

a. In words, define the random variable X.

b. What does it mean that the values zero, one, and two are not included for x in the PDF?

It has been estimated that only about 30% of California residents have adequate earthquake supplies. Suppose you randomly survey 11 California residents. We are interested in the number who have adequate earthquake supplies.

a. In words, define the random variable X.

b. List the values that X may take on.

c. Give the distribution of X. X ~ _____(_____,_____)

d. What is the probability that at least eight have adequate earthquake supplies?

e. Is it more likely that none or that all of the residents surveyed will have adequate earthquake supplies? Why?

f. How many residents do you expect will have adequate earthquake supplies?

Suppose that the PDF for the number of years it takes to earn a Bachelor of Science (B.S.) degree is given as in Table 4.34

On average, how many years do you expect it to take for an individual to earn a B.S.?
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