Explanation Given: The function is f ( x ) = { 1 − 1 2 x if 0 ≤ x ≤ 2 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 . Calculation: The probability density function of the continuous random variable X is f ( x ) = { 1 − 1 2 x if 0 ≤ x ≤ 2 0 otherwise

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Chapter 11, Problem 4RE

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To find: The probability P(0≤X≤1) and then illustrate with a graph.

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Chapter 11 Solutions

EP CALCULUS F/BUS.,ECON.-BRIEF-ACCESS

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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The probability P ( 0 ≤ X ≤ 1 ) and then illustrate with a graph.

Solution Summary: The author explains the probability density function of the continuous random variable X.

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To find: The probability P(0≤X≤1) and then illustrate with a graph.

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