Explanation Formula used: Normal probability density function: The function is f ( x ) = 1 σ 2 π e − ( x − μ ) 2 / 2 σ 2 , σ ≥ 0 . The median of normal probability density function is μ . Exponential Probability Density Function: The function is f ( x ) = { 1 λ e − x λ if x ≥ 0 0 otherwise . The median of Exponential probability density function is m = λ ln 2 . Calculation: The probability density functions are g 1 ( x ) = 1 2 π e − ( x − 1 ) 2 / 2 and g 2 ( x ) = { e − x if x ≥ 0 0 otherwise . The probability density function g 1 ( x ) = 1 2 π e − ( x − 1 ) 2 / 2 represents a standard normal distribution. By the above formula stated that, the median of the probability density function g 1 ( x ) = 1 2 π e − ( x − 1 ) 2 / 2 is 1. The probability density function of g 2 ( x ) = { e − x if x ≥ 0 0 otherwise represents an exponential distribution

14th Edition

ISBN: 9780135961438

Author: Barnett

Publisher: PEARSON CO

See similar textbooks

Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could co…

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a…

Videos

Question

Chapter 11.4, Problem 35E

To determine

To explain: The medians of the probability density functions from the graph of g1(x) and g2(x).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.4, Problem 34E

Chapter 11.4, Problem 36E

Students have asked these similar questions

Problems 4.2. Suppose that X is a continuous random variable with probability density function given by f(x) = x² + x + } for 0

2. If the random variable X has the probability density function f(x) = (1-x²), -1 < x < 1, 3 4 what is the variance of 15X + 2?

Problem 2 Consider a random variable with cdf(x) 1-exp(-10x) when x2 0. And 0 otherwise. a) Determine Pr{ X S4 } b) Pr{ X € (1, 4) } c) Find PDF(x)

Chapter 11 Solutions

EP CALCULUS FOR BUSINESS..-MYLAB ACCESS

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

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The medians of the probability density functions from the graph of g 1 ( x ) and g 2 ( x ) .

Solution Summary: The author explains the medians of the probability density functions from the graph of g_1(x) and

Concept explainers

Videos

To explain: The medians of the probability density functions from the graph of g1(x) and g2(x).

Want to see the full answer?

Chapter 11 Solutions