To determine To find: The expected value, the variance and the standard deviation. Explanation Given: The function f ( x ) = { x 3 12 if 0 ≤ x ≤ 2 16 3 x 3 if x > 2 is a probability density function. Definition used: If X is a continuous random variable with probability function f on [ a , b ] , then the expected value of X is E ( X ) = μ = ∫ a b x f ( x ) d x The variance of X is V a r ( X ) = ∫ a b x 2 f ( x ) d x − ( μ ) 2 . And the standard deviation value of X is σ ≈ V a r ( X ) . Calculation: Consider the given function f ( x ) = { x 3 12 if 0 ≤ x ≤ 2 16 3 x 3 if x > 2 Use the above mentioned definition and find expected value as follows, E ( X ) = μ = ∫ 0 ∞ x f ( x ) d x = ∫ 0 2 x f ( x ) d x + ∫ 2 ∞ x f ( x ) d x = ∫ 0 2 x ( x 3 12 ) d x + ∫ 2 ∞ x ( 16 3 x 3 ) d x On further simplification the above expression becomes, E ( X ) = 1 12 ∫ 0 2 x 4 d x + 16 3 ∫ 2 ∞ ( 1 x 2 ) d x = 1 12 [ x 5 5 ] 0 2 + 16 3 [

Calculus with Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Lial, Greenwell & Ritchey, The Applied Calculus & Finite Math Series)

11th Edition

ISBN: 9780133886832

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 11.2, Problem 21E

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To find: The expected value, the variance and the standard deviation.

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Chapter 11.2, Problem 20E

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Calculus with Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Lial, Greenwell & Ritchey, The Applied Calculus & Finite Math Series)

Ch. 11.1 - YOUR TURN 1 Repeat Example 1(a) for the function...Ch. 11.1 - Prob. 2YT Ch. 11.1 - Prob. 3YT Ch. 11.1 - Prob. 4YT Ch. 11.1 - Prob. 1WE Ch. 11.1 - Prob. 2WE Ch. 11.1 - Prob. 3WE Ch. 11.1 - Decide whether the functions defined as follows...Ch. 11.1 - Decide whether the functions defined as follows...Ch. 11.1 - Decide whether the functions defined as follows...

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