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CalculusCalculus10th Edition

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Chapter 8.8, Problem 80E
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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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Problem 77E
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Problem 79E
Problem 80E
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Problem 82E
Problem 83E
Problem 84E
Problem 85E
Problem 86E
Problem 87E
Problem 88E
Problem 89E
Problem 90E
Problem 91E
Problem 92E
Problem 93E
Problem 94E
Problem 95E
Problem 96E
Problem 97E
Problem 98E
Problem 99E
Problem 100E
Problem 101E
Problem 102E
Problem 103E
Problem 104E
Problem 105E
Problem 106E
Problem 107E
Problem 108E
Problem 109E
Problem 110E
Problem 111E
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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

In Exercises 79 and 80, (a) show that the nonnegative function is a probability density function, (b) find P(0 ≤ x ≤ 4), and (c) find E(x).

f ( t )     =     { 2 5 e − 2 t / 5 , t   ≥   0 0 , t   <   0

(a)

To determine

To prove: That the non-negative function f(t)={25e−2t/5,t≥00        t<0 is a probability density function.

Explanation

Given:

The function is f(t)={25e−2t/5,t≥00        t<0.

Formula used:

The formula for integration is:

∫eaxdx=eaxa

Where, a is a constant value and x is a variable.

Proof:

Let f(t)={25e−2t/5,t≥00        t<0

Therefore, find out ∫−∞∞f(t)dt for f(t)={25e−2t/5,t≥00        t<0.

Since, f(t)={25e−2t/5,t≥00        t<0 exists for t>0 as it is an exponential function

(b)

To determine

To calculate: The value of P(0≤x≤4) for f(t)={25e−2t/5,t≥00        t<0.

(c)

To determine

The value of E(x) for f(t)={25e−2t/5,t≥00        t<0.

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Chapter 8.8,
Problem 79E
Chapter 8.8,
Problem 81E
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Sect-8.1 P-1ESect-8.1 P-2ESect-8.1 P-3ESect-8.1 P-4ESect-8.1 P-5ESect-8.1 P-6ESect-8.1 P-7ESect-8.1 P-8ESect-8.1 P-9ESect-8.1 P-10E
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P-15RECh-8 P-16RECh-8 P-17RECh-8 P-18RECh-8 P-19RECh-8 P-20RECh-8 P-21RECh-8 P-22RECh-8 P-23RECh-8 P-24RECh-8 P-25RECh-8 P-26RECh-8 P-27RECh-8 P-28RECh-8 P-29RECh-8 P-30RECh-8 P-31RECh-8 P-32RECh-8 P-33RECh-8 P-34RECh-8 P-35RECh-8 P-36RECh-8 P-37RECh-8 P-38RECh-8 P-39RECh-8 P-40RECh-8 P-41RECh-8 P-42RECh-8 P-43RECh-8 P-44RECh-8 P-45RECh-8 P-46RECh-8 P-47RECh-8 P-48RECh-8 P-49RECh-8 P-50RECh-8 P-51RECh-8 P-52RECh-8 P-53RECh-8 P-54RECh-8 P-55RECh-8 P-56RECh-8 P-57RECh-8 P-58RECh-8 P-59RECh-8 P-60RECh-8 P-61RECh-8 P-62RECh-8 P-63RECh-8 P-64RECh-8 P-65RECh-8 P-66RECh-8 P-67RECh-8 P-68RECh-8 P-69RECh-8 P-70RECh-8 P-71RECh-8 P-72RECh-8 P-73RECh-8 P-74RECh-8 P-75RECh-8 P-76RECh-8 P-77RECh-8 P-78RECh-8 P-79RECh-8 P-80RECh-8 P-81RECh-8 P-82RECh-8 P-83RECh-8 P-84RECh-8 P-85RECh-8 P-86RECh-8 P-87RECh-8 P-88RECh-8 P-89RECh-8 P-90RECh-8 P-91RECh-8 P-1PSCh-8 P-2PSCh-8 P-3PSCh-8 P-4PSCh-8 P-5PSCh-8 P-6PSCh-8 P-7PSCh-8 P-8PSCh-8 P-9PSCh-8 P-10PSCh-8 P-11PSCh-8 P-12PSCh-8 P-13PSCh-8 P-14PSCh-8 P-15PSCh-8 P-16PSCh-8 P-17PSCh-8 P-18PSCh-8 P-19PSCh-8 P-20PSCh-8 P-21PSCh-8 P-22PS

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