(a) Explanation Given information: The given function is f ( x ) = π 20 sin ( π x 10 ) , if 0 ≤ x ≤ 10 and f ( x ) = 0 if x < 0 or x > 10 Calculation: Show the function as follows: f ( x ) = π 20 sin ( π x 10 ) (1) Show the conditions of probability density function as follows: (A) The probability density function f of a random variable X satisfies the condition f ( x ) ≥ 0 for all x . (B) The probabilities are measured on a scale from 0 to 1, it follows that ∫ − ∞ ∞ f ( x ) d x = 1 . Apply the probability density function (B) in Equation (1) as shown below (b) To determine To calculate: The value of P ( X < 4 ) . (c) To determine To calculate: The value of mean

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Chapter 8, Problem 21E

(a)

To determine

To explain: the given function as probability density function with explanation.

(b)

To determine

To calculate: The value of P(X<4) .

(c)

To determine

To calculate: The value of mean

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Chapter 8, Problem 20E

Chapter 8, Problem 22E

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the given function as probability density function with explanation.

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To explain: the given function as probability density function with explanation.

To calculate: The value of P(X<4) .

To calculate: The value of mean

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Chapter 8 Solutions