Let N denotes the normally distributed random variable with E[N] = m Var[N] = 0² a) Show the E[L] = exp(E[N] +0.5 Var[N]) = exp (m+ 0.50²) Hint: Start with the probability density function for N: p(x) = (1/(sqrt (2π) σ)) exp( −((x −m)² / (20²))) and use the fact that E[L] = S x p(x) dx b) Obtain the formula for Var[L] in terms of m and σ. Workout E[1/L]. Is it true that E[1/L] = 1/E[L] Let X be a random variable that taken only positive values. Let q(x) denote its pdf. Using integrals, write down the expression equivalent to the condition: E[1/X] =1/E[X] c)
Let N denotes the normally distributed random variable with E[N] = m Var[N] = 0² a) Show the E[L] = exp(E[N] +0.5 Var[N]) = exp (m+ 0.50²) Hint: Start with the probability density function for N: p(x) = (1/(sqrt (2π) σ)) exp( −((x −m)² / (20²))) and use the fact that E[L] = S x p(x) dx b) Obtain the formula for Var[L] in terms of m and σ. Workout E[1/L]. Is it true that E[1/L] = 1/E[L] Let X be a random variable that taken only positive values. Let q(x) denote its pdf. Using integrals, write down the expression equivalent to the condition: E[1/X] =1/E[X] c)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Please provide explanantion
![Let N denotes the normally distributed random variable with
E[N] = m
Var[N] =²
a) Show the E[L] = exp(E[N] +0.5 Var[N]) = exp (m+ 0.50²) Hint: Start with the probability density
function for N: p(x) = (1/(sqrt (2µ) σ)) exp( −((x − m)² / (20²))) and use the fact that
E[L] = S x p(x) dx
Obtain the formula for Var[L] in terms of m and σ. Workout E[1/L]. Is it true that E[1/L] = 1/E[L]
Let X be a random variable that taken only positive values. Let q(x) denote its pdf. Using
integrals, write down the expression equivalent to the condition: E[1/X] = 1/E[X]
b)
c)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F00828718-2df8-4d22-87de-a2e53e10f924%2F383a1f39-7667-4044-ab93-794098fa98ec%2Fafcffck_processed.png&w=3840&q=75)
Transcribed Image Text:Let N denotes the normally distributed random variable with
E[N] = m
Var[N] =²
a) Show the E[L] = exp(E[N] +0.5 Var[N]) = exp (m+ 0.50²) Hint: Start with the probability density
function for N: p(x) = (1/(sqrt (2µ) σ)) exp( −((x − m)² / (20²))) and use the fact that
E[L] = S x p(x) dx
Obtain the formula for Var[L] in terms of m and σ. Workout E[1/L]. Is it true that E[1/L] = 1/E[L]
Let X be a random variable that taken only positive values. Let q(x) denote its pdf. Using
integrals, write down the expression equivalent to the condition: E[1/X] = 1/E[X]
b)
c)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman