Explanation Approach: The Probability Density Function on [ a , b ] for the function f is defined as, f ( x ) ≥ 0 for all x in the interval [ a , b ] ∫ a b f ( x ) d x = 1 P ( c ≤ X ≤ d ) = ∫ c d f ( x ) d x for c , d in [ a , b ] Calculation: Consider, the probability density function f ( x ) = k x with the interval [ 4 , 9 ] . The given function f ( x ) ≥ 0 is always positive in the interval [ 4 , 9 ] . Integrate the function f ( x ) = k x in the domain [ 4 , 9 ] , ∫ 4 9 f ( x ) d x = ∫ 4 9 ( k x ) d x = k [ x 1 2 + 1 1 2

2nd Edition

ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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 13.CR, Problem 20CR

To determine

To find:

The value of k that will make f(x)=kx define a probability density function for the indicated interval [4,9].

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.CR, Problem 19CR

Chapter 13.CR, Problem 21CR

Students have asked these similar questions

a) Find k such that the function is a probability density function over the given interval. b) Then write the probability density function. ƒ(x) = [5, 20] k -, X

Let X be a continuous random variable with probability density function 1 f (x) : T(1+ x2) Define Y 4. What is the mean of y?

Let X be the number of minutes that it takes a random selected student to solve a mathematical problem. The probability density function of X is: 1)Find the mean of X. 2) Find the standard deviation of X.

Chapter 13 Solutions

Calculus For The Life Sciences

Ch. 13.1 - Repeat Example 1a for the function f(x)=2x2 on...Ch. 13.1 - Prob. 2YT Ch. 13.1 - Prob. 3YT Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E

Knowledge Booster

$Calculus$

Learn more about

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

The value of k that will make f ( x ) = k x define a probability density function for the indicated interval [ 4 , 9 ] .

Solution Summary: The author explains the probability density function f(x)=ksqrtx for the indicated interval.

Concept explainers

Videos

To find:

The value of k that will make f(x)=kx define a probability density function for the indicated interval [4,9].

Want to see the full answer?

Chapter 13 Solutions

The value of k that will make f ( x ) = k x define a probability density function for the indicated interval [ 4 , 9 ] .

Solution Summary: The author explains the probability density function f(x)=ksqrtx for the indicated interval.

Concept explainers

Videos

To find: The value of k that will make f(x)=kx define a probability density function for the indicated interval [4,9].

Want to see the full answer?

Chapter 13 Solutions

To find:

The value of k that will make f(x)=kx define a probability density function for the indicated interval [4,9].