The pdf (probability density function) for the CONTINUOUS random variable X is given as: f(x) = { (1/5)e^(-x/5); x>0 ] 0; elsewhere a. Show that f(x) satisfies the properties for a pdf, and state your justification for the conditions. b. Find the CDF of X. c. Find P (x ≥ 5) using pdf and CDF

The pdf (probability density function) for the CONTINUOUS random variable X is given as: f(x) = { (1/5)e^(-x/5); x>0 ] 0; elsewhere a. Show that f(x) satisfies the properties for a pdf, and state your justification for the conditions. b. Find the CDF of X. c. Find P (x ≥ 5) using pdf and CDF

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

The pdf (probability density function) for the CONTINUOUS random variable X is given as:

f(x) = { (1/5)e^(-x/5); x>0 ]

0; elsewhere

a. Show that f(x) satisfies the properties for a pdf, and state your justification for the conditions.

b. Find the CDF of X.

c. Find P (x ≥ 5) using pdf and CDF.

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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