E(Y) = a+ bE(X)+ c[E(x)]² + cVar(X) when X is a discrete random variable. You must use the definition of Expectation of a function of a discrete random variable, (summation operators and indicating at each step why you substitute)as we did in all the proofs of this lecture. Repeat (a) but assuming that X is continuous, in which case you will be using the integration operator.

E(Y) = a+ bE(X)+ c[E(x)]² + cVar(X) when X is a discrete random variable. You must use the definition of Expectation of a function of a discrete random variable, (summation operators and indicating at each step why you substitute)as we did in all the proofs of this lecture. Repeat (a) but assuming that X is continuous, in which case you will be using the integration operator.

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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Question

The random variable X is given and we define a new random variable
Y = g(X)Og(x) = a + bx + cx². In this problem, you will do,showing
detail work, and the definition of expectation of a function of a random
variable (i.e., definition of E(g(X))):
Show that
E(Y) = a+ bE(X)+ c[E(x)]² + cVar(X)
when X is a discrete random variable. You must use the definition of
Expectation of a function of a discrete random variable, (summation
operators and indicating at each step why you substitute)as we did
in all the proofs of this lecture.
O Repeat (a) but assuming that X is continuous, in which case you will
be using the integration operator.
(b)

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