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Chapter 5: Q.7 (page 346)

What is the area under f(x) if the function is a continuous probability density function?

Short Answer

Expert verified

The area under f(x) will be 1 if the function is continuous probability density function

Step by step solution

01

Given information

Given in the question that statement the function is a continuous probability density function

02

Solution

It is understood that if a continuous probability density is merged on its entire limit, the resultant value is always 1, hence the area under f(x) will be 1.

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Most popular questions from this chapter

In major league baseball, a no-hitter is a game in which a pitcher, or pitchers, doesn't give up any hits throughout the game. No-hitters occur at a rate of about three per season. Assume that the duration of time between no-hitters is exponential.

a. What is the probability that an entire season elapses with a single no-hitter?

b. If an entire season elapses without any no-hitters, what is the probability that there are no no-hitters in the following season?

c. What is the probability that there are more than 3 no-hitters in a single season?

Find the amount (percent of one gram) of carbon-14 lasting less than 5,730 years. This means, find P(x < 5,730).

a. Sketch the graph, and shade the area of interest

b. Find the probability. P(x < 5,730) = __________

Use the following information to answer the next three exercises.

The Sky Train from the terminal to the rental–car and long–term parking center is supposed to arrive every eight minutes. The waiting times for the train are known to follow a uniform distribution.

80. Find the 30thpercentile for the waiting times (in minutes).

a. two

b.2.4

c.2.75

d. three

Use the following information to answer the next eleven exercises. The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years.

What is being measured here?

Use the following information to answer the next ten exercises. A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by the following distribution: X~Exp(0.2)

Are outcomes equally likely in this distribution? Why or why not?
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