Explanation Given: The function f ( x ) = e − x 2 . 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 given function is f ( x ) = e − x 2 . The function f is a probability density function of the continuous random variable X only if it satisfies the first two condition of the above definition. The range of the function f ( x ) = e − x 2 is greater than 0

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Chapter 11, Problem 11RE

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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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To check: Whether f is a probability density function or not if f ( x ) = e − x 2 .

Solution Summary: The author explains that the function f(x) is not a probability density function.

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To check: Whether f is a probability density function or not if f(x)=e−x2.

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Chapter 11 Solutions