Explanation Given: The function is, f ( x ) = { e − x 3 if x ≥ 0 0 otherwise . Definition used: Probability Density Function: “The function f ( x ) is a probability density function for a continuous random variable X if, 1. f ( x ) ≥ 0 for all x ∈ ( − ∞ , ∞ ) . 2. ∫ − ∞ ∞ f ( x ) d x = 1 . 3. The probability that X lies in the interval [ c , d ] is given by P ( c ≤ X ≤ d ) = ∫ c d f ( x ) d x ”. Proof: Assume k f ( x ) is probability density function. Compute the value of k by using the above definition

Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)

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ISBN: 9780137400126

Author: Raymond Barnett, Michael Ziegler

Publisher: PEARSON+

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Chapter 11.2, Problem 41E

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To find: A constant k such that kf is a probability density or if no such constant exists, then explain the reason.

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Chapter 11.2, Problem 40E

Chapter 11.2, Problem 42E

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What is a solution to a differential equation? We said that a differential equation is an equation that describes the derivative, or derivatives, of a function that is unknown to us. By a solution to a differential equation, we mean simply a function that satisfies this description. 2. Here is a differential equation which describes an unknown position function s(t): ds dt 318 4t+1, ds (a) To check that s(t) = 2t2 + t is a solution to this differential equation, calculate you really do get 4t +1. and check that dt' (b) Is s(t) = 2t2 +++ 4 also a solution to this differential equation? (c) Is s(t)=2t2 + 3t also a solution to this differential equation? ds 1 dt (d) To find all possible solutions, start with the differential equation = 4t + 1, then move dt to the right side of the equation by multiplying, and then integrate both sides. What do you get? (e) Does this differential equation have a unique solution, or an infinite family of solutions?

Chapter 11 Solutions

Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)

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

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A constant k such that kf is a probability density or if no such constant exists, then explain the reason.

Solution Summary: The author explains that if kf is a probability density, then explain the reason.

To find: A constant k such that kf is a probability density or if no such constant exists, then explain the reason.

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Chapter 11 Solutions