2. We want to measure the diameter of a cell using some equipment. Suppose the diameter of the cell X follows a uniform prior X~ U(0, 1). Let Y denote the measurement we get from the equipment. Due to the inaccuracy of the measurement, give X = x, Y follows a uniform distribution U(x-0.2,x+0.2). Based on the measurement Y we observe, we want to use the least mean square estimation rule to estimate X. (a) Suppose we observe that Y = 0.4 i. Find the possible range of random variable X. ii. Find the LMS estimation LMS (0.4). iii. Find the corresponding conditional MSE given Y = 0.4 (b) Suppose we observe that Y = 1.1 i. Find the possible range of random variable X. ii. Find the LMS estimation LMS (1.1). iii. Find the corresponding conditional MSE given Y = 1.1 Give your answers to four decimal places.
2. We want to measure the diameter of a cell using some equipment. Suppose the diameter of the cell X follows a uniform prior X~ U(0, 1). Let Y denote the measurement we get from the equipment. Due to the inaccuracy of the measurement, give X = x, Y follows a uniform distribution U(x-0.2,x+0.2). Based on the measurement Y we observe, we want to use the least mean square estimation rule to estimate X. (a) Suppose we observe that Y = 0.4 i. Find the possible range of random variable X. ii. Find the LMS estimation LMS (0.4). iii. Find the corresponding conditional MSE given Y = 0.4 (b) Suppose we observe that Y = 1.1 i. Find the possible range of random variable X. ii. Find the LMS estimation LMS (1.1). iii. Find the corresponding conditional MSE given Y = 1.1 Give your answers to four decimal places.
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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Please show work for part a or b.
But please make it complete. Thanks
Transcribed Image Text:2. We want to measure the diameter of a cell using some equipment. Suppose the diameter of
the cell X follows a uniform prior X~ U(0, 1). Let Y denote the measurement we get from
the equipment. Due to the inaccuracy of the measurement, give X = x, Y follows a uniform
distribution U(x-0.2, x+0.2). Based on the measurement Y we observe, we want to use the
least mean square estimation rule to estimate X.
(a) Suppose we observe that Y = 0.4
i. Find the possible range of random variable X.
ii. Find the LMS estimation LMS(0.4).
iii. Find the corresponding conditional MSE given Y = 0.4
(b) Suppose we observe that Y = 1.1
i. Find the possible range of random variable X.
ii. Find the LMS estimation LMS (1.1).
iii. Find the corresponding conditional MSE given Y = 1.1
Give your answers to four decimal places.
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