1. Suppose that X is a random variable with pdf: f(x) = (2x + 1)/6, 0 < x < 2. (a)Find the cdf . Give the complete cdf for any real value of x. (b)Find the mean and variance of X. (c)Verify that Chebyshev’s Theorem holds for k = 5/3. (d) Find P(0.10 < X < 0.50) using the cdf in (a).

1. Suppose that X is a random variable with pdf: f(x) = (2x + 1)/6, 0 < x < 2. (a)Find the cdf . Give the complete cdf for any real value of x. (b)Find the mean and variance of X. (c)Verify that Chebyshev’s Theorem holds for k = 5/3. (d) Find P(0.10 < X < 0.50) using the cdf in (a).

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

#1.

Suppose that X is a random variable with pdf: f(x) = (2x + 1)/6, 0 < x < 2.

(a)Find the cdf . Give the complete cdf for any real value of x.

(b)Find the mean and variance of X.

(c)Verify that Chebyshev’s Theorem holds for k = 5/3.

(d) Find P(0.10 < X < 0.50) using the cdf in (a).

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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