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.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 94E

See similar textbooks