a. Explanation Given: The probability density function f ( x ) = 1 4 x on the interval [ 1 , 9 ] . Definition used: “A probability density function of a random variable X in an interval I , where I may be bounded or unbounded is a nonnegative function f having the following properties. 1. The total area of the region under the graph of f is equal to 1. 2. The probability that an observed value of the random variable X lies in the interval [ a , b ] is P ( a ≤ X ≤ b ) = ∫ a b f ( x ) d x .” Calculation: Use the definition stated above, the probability P ( X ≥ 4 ) is computed as follows, P ( X ≥ 4 ) = ∫ 4 9 1 4 x d x = 1 4 b. To determine To find: The probability P ( 1 ≤ X < 8 ) . c. To determine To find: The probability P ( X = 3 ) . d. To determine To find: The probability P ( X ≤ 4 ) .

APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI

10th Edition

ISBN: 9780357465400

Author: Tan

Publisher: CENGAGE L

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Chapter 10.1, Problem 23E

To determine

To find: The probability P(X≥4) .

To determine

To find: The probability P(1≤X<8) .

To determine

To find: The probability P(X=3) .

To determine

To find: The probability P(X≤4) .

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Chapter 10.1, Problem 22E

Chapter 10.1, Problem 24E

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Chapter 10 Solutions

APPLIED CALCULUS FOR MGRL, LIFE, SOC SCI

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The probability P ( X ≥ 4 ) .

Solution Summary: The author explains the probability density function f(x)=14sqrtx

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To find: The probability P(X≥4) .

To find: The probability P(1≤X<8) .

To find: The probability P(X=3) .

To find: The probability P(X≤4) .

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Chapter 10 Solutions