f (x) = 4xc for 0 ≤ x ≤ 1 ; Find the constant c so that f (x) is a pdf of some random variable X, and then find the cdf, F (x) = P(X ≤ x). Sketch graphs of the pdf f (x) and the cdf F (x), and find the mean μ and variance σ2.

f (x) = 4xc for 0 ≤ x ≤ 1 ; Find the constant c so that f (x) is a pdf of some random variable X, and then find the cdf, F (x) = P(X ≤ x). Sketch graphs of the pdf f (x) and the cdf F (x), and find the mean μ and variance σ2.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

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Question

f (x) = 4x^c for 0 ≤ x ≤ 1 ; Find the constant c so that f (x) is a
pdf of some random variable X, and then find the cdf, F (x) = P(X ≤ x). Sketch graphs
of the pdf f (x) and the cdf F (x), and find the mean μ and variance σ².

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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