Let f(x) = k(3x - x²) if 0 ≤ x ≤ 3 and f(x) = 0 if x <0 or x > 3.a) For what value of k is f a probability density function?b) For that value of k, find P(X > 1).

Answered: Image /qna-images/answer/c4d13364-7ea9-4087-9609-2d7b8224eaf5.jpg

Answered: Let f(x) = k(3x - x²) if 0 ≤ x ≤ 3 and…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Similar questions

Let X be a discrete random variable with probability density function: FUNCTION IS IN THE IMAGE Find C. Find P(X < 2). Find E(X). Find V(X).
H/W: if X andY are continuous random variables, prove E[X] = E[E[X|Y]]?
Find a value of k that will make fa probability density function on the indicated interval. f(x) = kx, [1, 4] k = (Type an integer or a simplified fraction.)
Show that if g is a density function, then Pg(·) is a countably additive probability on B.
Consider the probability density function 0 if x 4. Find E(X). Select one: 37 27 - 32 27 13 27
SHOW ONLY THE SET-UP FORMULA AND GRAPH IT
Suppose a random variable X has a probability density function given by O elsewhere f (x) = kx (1 − x) 0 ≤ x ≤ 1 0 elsewhere a. Find the value of k that makes this a probability density function b. Find P (0.4 ≤ x ≤ 1) c. Find P(x ≤ 0.4) d. Find P (0.8 ≤ x))
Let XE {-1,0, 1} . That is, X is a discrete random variable only takes three values -1, 0, and 1. Suppose the equality for Chebyshev's inequality holds for X and P(X = 0) = 0.3 , find P(X = 1) Let X be a random variable with probability density f(x) = x6 for x > 1 and O else. Use Chebyshev's inequality to bound P(X > 2.5) . Round your answer to 3 decimal places.
Consider a constant function: f(x)= c; a ≤ x ≤ b Suppose that the function represents a probability density function and c<1 , which of the following is true? a. |a−b|<0 b. |a−b|<1 c. |a−b|>1 d. |a−b|=1
A random variable X has a probability density function equal toWhere p is a constant in the interval [0, 1] and C is another constant. Ask:a) Find C so that fX (x) is a probability density function valid.b) Determine the generator function of moments MX(s) of V.A. X.c) Use MX(s) to calculate E{X}.d) Use MX(s) to calculate E {X2}e) Determine the variance of X.

Recommended textbooks for you

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781319050740

Author:

Jon Rogawski, Colin Adams, Robert Franzosa

Publisher:

W. H. Freeman

Precalculus

Calculus

ISBN:

9780135189405

Author:

Michael Sullivan

Publisher:

PEARSON

Calculus: Early Transcendental Functions

Calculus

ISBN:

9781337552516

Author:

Ron Larson, Bruce H. Edwards

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

Let f(x) = k(3x - x²) if 0 ≤ x ≤ 3 and f(x) = 0 if x <0 or x > 3. a) For what value of k is f a probability density function? b) For that value of k, find P(X > 1).