Explanation Formula used: Let f ( x ) be a uniform probability density function for a continuous random variable X then, f ( x ) = { 1 b − a if a ≤ x ≤ b 0 otherwise Expected value or mean ( µ ): μ = 1 2 ( a + b ) Calculation: Let X be continuous random variable that is uniformly distributed on the interval [ 0 , 10 ] . Substitute the values of a and b in the formula for the uniform density function as, f ( x ) = 1 b − a = 1 10 − 0 = 1 10 Thus, the uniform density function is f ( x ) = { 1 10 if 0 ≤ x ≤ 10 0 otherwise

17th Edition

ISBN: 9781323520192

Author: Pearson

Publisher: PEARSON C

See similar textbooks

Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could co…

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a…

Videos

Question

Chapter 11.4, Problem 38E

To determine

To find: The mean µ and then the probability P(X≤μ).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.4, Problem 37E

Chapter 11.4, Problem 39E

Students have asked these similar questions

A smallish urn contains 25 small plastic bunnies – 7 of which are pink and 18 of which are white. 10 bunnies are drawn from the urn at random with replacement, and X is the number of pink bunnies that are drawn. (a) P(X = 5) ≈ (b) P(X<6) ≈ The Whoville small urn contains 100 marbles – 60 blue and 40 orange. The Grinch sneaks in one night and grabs a simple random sample (without replacement) of 15 marbles. (a) The probability that the Grinch gets exactly 6 blue marbles is [ Select ] ["≈ 0.054", "≈ 0.043", "≈ 0.061"] . (b) The probability that the Grinch gets at least 7 blue marbles is [ Select ] ["≈ 0.922", "≈ 0.905", "≈ 0.893"] . (c) The probability that the Grinch gets between 8 and 12 blue marbles (inclusive) is [ Select ] ["≈ 0.801", "≈ 0.760", "≈ 0.786"] . The Whoville small urn contains 100 marbles – 60 blue and 40 orange. The Grinch sneaks in one night and grabs a simple random sample (without replacement) of 15 marbles. (a)…

Using Karnaugh maps and Gray coding, reduce the following circuit represented as a table and write the final circuit in simplest form (first in terms of number of gates then in terms of fan-in of those gates).

Consider the alphabet {a, b, c}.• Design a regular expression that recognizes all strings over {a, b, c} that have at least three nonconsec-utive c characters (two characters are non-consecutive if there is at least one character between them)and at least one a character.• Explain how your regular expression recognizes the string cbbcccac by clearly identifying which partsof the string match to the components of your regular expression

Chapter 11 Solutions

FIN 108 ISU LOOSE >IP<

Ch. 11.1 - Evaluate the following, if it converges: 3dx(x1)2.Ch. 11.1 - Prob. 2MP Ch. 11.1 - Prob. 3MP Ch. 11.1 - Prob. 4MP Ch. 11.1 - Prob. 5MP Ch. 11.1 - Prob. 6MP Ch. 11.1 - Prob. 1ED Ch. 11.1 - Prob. 2ED Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The mean µ and then the probability P ( X ≤ μ ) .

Solution Summary: The author explains how to find the mean and probability of a continuous random variable X.

Concept explainers

Videos

To find: The mean µ and then the probability P(X≤μ).

Want to see the full answer?

Chapter 11 Solutions