3. Let X; N iid U(0, 1) for i e {1, 2, ...,n}. (a) Compute the pdf of Y; = - log(X;), name the distribution that Y; follows and provide any parameter value or values needed. (b) Compute the pdf that W [I", X, = X1 X2... X, follows. You may use the result given as part of the Example 2.6 video (even though it will only be proved in Chapter 3). (c) Compute E[W] in the two following ways: (i) through exploiting independence of the X, and using EUV] = E[U]E[V] for any independent random variables U and V. (ii) using the pdf of W computed in the previous part.
3. Let X; N iid U(0, 1) for i e {1, 2, ...,n}. (a) Compute the pdf of Y; = - log(X;), name the distribution that Y; follows and provide any parameter value or values needed. (b) Compute the pdf that W [I", X, = X1 X2... X, follows. You may use the result given as part of the Example 2.6 video (even though it will only be proved in Chapter 3). (c) Compute E[W] in the two following ways: (i) through exploiting independence of the X, and using EUV] = E[U]E[V] for any independent random variables U and V. (ii) using the pdf of W computed in the previous part.
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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![3. Let X; N
iid
U(0, 1) for i e {1, 2, ...,n}.
(a) Compute the pdf of Y; = - log(X;), name the distribution that Y; follows and
provide any parameter value or values needed.
(b) Compute the pdf that W = [I", X, = X1 X2... X, follows. You may use the
result given as part of the Example 2.6 video (even though it will only be proved
in Chapter 3).
(c) Compute E[W] in the two following ways: (i) through exploiting independence of
the X, and using EUV] = E[U]E[V] for any independent random variables U
and V. (ii) using the pdf of W computed in the previous part.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2a398c26-6abf-4ee8-a36f-aa14e93f068a%2Fd180f4d8-f3e3-4053-a2e5-abd216aeab66%2F33fgtoo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Let X; N
iid
U(0, 1) for i e {1, 2, ...,n}.
(a) Compute the pdf of Y; = - log(X;), name the distribution that Y; follows and
provide any parameter value or values needed.
(b) Compute the pdf that W = [I", X, = X1 X2... X, follows. You may use the
result given as part of the Example 2.6 video (even though it will only be proved
in Chapter 3).
(c) Compute E[W] in the two following ways: (i) through exploiting independence of
the X, and using EUV] = E[U]E[V] for any independent random variables U
and V. (ii) using the pdf of W computed in the previous part.
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