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7. Suppose that X- Normal (u,o²). (a) Find the PDF fy(y) of Y = e, and then sketch the graph of fy in the special case that u =0 and o = 1 (when X is standard Normal). Note: This distribution is called Log-Normal(µ,o) %3D (b) Show that 1/Y is Log-Normal(-u,o

7. Suppose that X- Normal (u,o²). (a) Find the PDF fy(y) of Y = e, and then sketch the graph of fy in the special case that u =0 and o = 1 (when X is standard Normal). Note: This distribution is called Log-Normal(µ,o) %3D (b) Show that 1/Y is Log-Normal(-u,o

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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6. Using Poisson approximation, Estimate HOM I8ige a cia33 Iccas to De DO . with probability > 99.9% some pair of students have the same birthday. Note: Assume for simplicity that each student is equally likely to have been born on any one of the 365 days in a year (ignoring leap years). Hint: If there are n students, then there are () n²/2 pairs of students. Pairs of students are not independent, however, they are approximately so. Use Poisson approximation to estimate the probability that no pair of students share the same birthday. 7. Suppose that X~ Normal (u, o'). (a) Find the PDF fy (y) of Y = e, and then sketch the graph of fy in the special case that u Note: This distribution is called Log-Normal(H,o. :0 and o = 1 (when X is standard Normal). (b) Show that 1/Y is Log-Normal(-u,o, 2 Recommended (not to be handed in) • From C. M. Grinstead & J. L. Snell : §5.1 Exercises: 1-14, 16-45
Transcribed Image Text:6. Using Poisson approximation, Estimate HOM I8ige a cia33 Iccas to De DO . with probability > 99.9% some pair of students have the same birthday. Note: Assume for simplicity that each student is equally likely to have been born on any one of the 365 days in a year (ignoring leap years). Hint: If there are n students, then there are () n²/2 pairs of students. Pairs of students are not independent, however, they are approximately so. Use Poisson approximation to estimate the probability that no pair of students share the same birthday. 7. Suppose that X~ Normal (u, o'). (a) Find the PDF fy (y) of Y = e, and then sketch the graph of fy in the special case that u Note: This distribution is called Log-Normal(H,o. :0 and o = 1 (when X is standard Normal). (b) Show that 1/Y is Log-Normal(-u,o, 2 Recommended (not to be handed in) • From C. M. Grinstead & J. L. Snell : §5.1 Exercises: 1-14, 16-45
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