5. We know that the MMSE of Y given X is given by g(X) = E[Y|X]. We also know that the LLSE (Linear Least Square Estimate) of Y given X, denoted by L[Y|X], is shown as follows: Cov(X, Y) Var (X) (X - E(X)). L[Y|X] = E(Y) + Now we wish to estimate the probability of landing heads, denoted by 0, of a biased coin. We model as the value of a random variable with a known prior with PDF fe Unif(0, 1).. We consider n independent tosses and let X be the number of heads observed. (a) (b) Show that E[(- E[O[X])h(X)] = 0 for any real function h(.). Find the MMSE E[X] and the LLSE L[X]. (Eve's law: Var(Y) = E[Var(Y|X)] + Var[E(Y|X)].) ~

5. We know that the MMSE of Y given X is given by g(X) = E[Y|X]. We also know that the LLSE (Linear Least Square Estimate) of Y given X, denoted by L[Y|X], is shown as follows: Cov(X, Y) Var (X) (X - E(X)). L[Y|X] = E(Y) + Now we wish to estimate the probability of landing heads, denoted by 0, of a biased coin. We model as the value of a random variable with a known prior with PDF fe Unif(0, 1).. We consider n independent tosses and let X be the number of heads observed. (a) (b) Show that E[(- E[O[X])h(X)] = 0 for any real function h(.). Find the MMSE E[X] and the LLSE L[X]. (Eve's law: Var(Y) = E[Var(Y|X)] + Var[E(Y|X)].) ~

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 93E

See similar textbooks