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For each of the density functions of a continuous random variable X shown below, find (a) the mode. (b) the median, and (c) the mean. [1] 2 [3] f(x) = f(x) = f(x) = 625 14*(1-x²) -0.2 ≤ ≤1 otherwise 0.9391 sin(√2x - 1) 0.8 ≤ x ≤ 2.2 otherwise (0.9062 cos(1-√3x) -0.1 ≤x≤1.4 otherwise

For each of the density functions of a continuous random variable X shown below, find (a) the mode. (b) the median, and (c) the mean. [1] 2 [3] f(x) = f(x) = f(x) = 625 14*(1-x²) -0.2 ≤ ≤1 otherwise 0.9391 sin(√2x - 1) 0.8 ≤ x ≤ 2.2 otherwise (0.9062 cos(1-√3x) -0.1 ≤x≤1.4 otherwise

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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For each of the density functions of a continuous random variable X shown below, find (a) the mode. (b) the median, and (c) the mean. x(1-x²) -0.2 ≤ x ≤ 1 [1] [2] f(x) = f(x) = 625 144 otherwise 0.9391 sin(√2x - 1) 0.8 ≤ x ≤ 2.2 otherwise (0.9062 0.9062 cos(1-√3x) -0.1 ≤x≤1.4 otherwise
Transcribed Image Text:For each of the density functions of a continuous random variable X shown below, find (a) the mode. (b) the median, and (c) the mean. x(1-x²) -0.2 ≤ x ≤ 1 [1] [2] f(x) = f(x) = 625 144 otherwise 0.9391 sin(√2x - 1) 0.8 ≤ x ≤ 2.2 otherwise (0.9062 0.9062 cos(1-√3x) -0.1 ≤x≤1.4 otherwise
Expert Solution
Step 1 Given Data:

Here 3 density function with continuous random variable X is given.

(1)The mode of x for continuous random variable can be given by,

f'(x)=0

it gives the maximum value of the function.

(2) The median of the density function is given by,

∫-∞cf(x)dx=0.5

(3)If x is a continuous random variable, then the mean of x is given by,

Ex=∫-∞∞xf(x) dx

 

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