Explanation Given: The function is f ( x ) = 2 x e − x 2 for x ≥ 0 . Definition used: “Cumulative distribution function: If f is a probability density function of a random variable in the interval [ a , b ] , then the cumulative distribution function is defined as F ( x ) = P ( X ≤ x ) = ∫ a x f ( t ) d t for x ≥ a . Also F ( x ) = 0 for x < a .” Calculation: Use the above mentioned definition and find the Cumulative distribution function. F ( x ) = P ( X ≤ x ) = ∫ 0 x 2 t e − t 2 d t The indefinite integral is ∫ 2 t e − t 2 d t . Let, u = − t 2 . Differentiate u = − t 2 with respect to t . d d t ( u ) = d d t ( − t 2 ) d u d t = − 2 t d u = − 2 t d t Substitute u = − t 2 and d u = − 2 t d t to compute the indefinite integral

Calculus With Applications, Books a la Carte Plus MyLab Math Package (11th Edition)

11th Edition

ISBN: 9780133886849

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

See similar textbooks

Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear re…

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Videos

Question

Chapter 11.1, Problem 4YT

To determine

To find: The probability of a bird’s nest within 1 km of the point zero.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.1, Problem 3YT

Chapter 11.1, Problem 1WE

Students have asked these similar questions

Inverse laplace transform Lect: Huda I H.w 1- F(S)= A- Find - F(s) of the following S (s+1)5 1 2- F(s) s² (s-a) 5+5 3- F(s)= s2+4s+3 1 4- F(s)= (s+2)2(s-2) 3s2-7s+5 5- F(s)= (s-1)(s2-5s+6)

Inverse laplace transform Lect :Huda I H.w A- Find L-1 F(s) of the following 1- F(S)= 2- F(s)- S (+1)5 s² (s-a) 5+5 s2+4s+3 3- F(s)- 1 4- F(s)- (s+2)2(s-2) 3s2-7s+5 5- F(s)- (s-1)(s2-55+6) B-Solve the D.E of the following: 1- y'+3y+2fy dt = f(t) for y(0)-1 if f(t) is the function whose graph is shown below 2 1 2 2-y+4y-u(t) for y(0)=y'(0)=0 3- y"+4y'+13y= e−2t sin3t for y(0)-1 and y'(0)=-2 17

show step by step answer

Chapter 11 Solutions

Calculus With Applications, Books a la Carte Plus MyLab Math Package (11th Edition)

Ch. 11.1 - YOUR TURN 1 Repeat Example 1(a) for the function...Ch. 11.1 - Prob. 2YT Ch. 11.1 - Prob. 3YT Ch. 11.1 - Prob. 4YT Ch. 11.1 - Prob. 1WE Ch. 11.1 - Prob. 2WE Ch. 11.1 - Prob. 3WE Ch. 11.1 - Decide whether the functions defined as follows...Ch. 11.1 - Decide whether the functions defined as follows...Ch. 11.1 - Decide whether the functions defined as follows...

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.