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

See similar textbooks

Similar questions

Consider a function F (x ) = 0, if x < 0 F (x ) = 1 − e^(−x) , if x ≥ 0 Is the corresponding random variable continuous?
The diameter of a round rock in a bucket, can be messured in mm and considered a random variable X in f(x) f(x) = k(x-x4) if 0 ≤ x ≤ 1f(x) = 0 otherwise. Find the expectation E(4X+ 3) and variance V(4X+3)
Let X be a Poisson random variable with E(X) = 3. Find P(2 < x < 4).
X1 and X2 are independent random variables such that Xi has PDF fXi(x)={λiexp(−λix) when x≥0, 0 otherwise}. What is P[X2<X1]?
If X and Y are independent Poisson random variables with E[X] = 3 and E[Y] = 2, what is P[ X = 2 | X + Y = 4 ]?
If X is Poisson random variable with parameter λ, compute E[1/(X + 1)]
(b) Let Z be a discrete random variable with E(Z) = 0. Does it necessarily follow that E(Z³) = 0? If yes, give a proof; if no, give a counterexample.
The diameter of a round rock in a bucket, can be messured in mm and considered a random variable X in f(x) f(x) = k(x-x4) if 0 ≤ x ≤ 1f(x) = 0 otherwise. Find the expectation E(X) and variance V(X)
A certain brand of upright freezer is available in threedifferent rated capacities: 16 ft3, 18 ft3, and 20 ft3. LetX = the rated capacity of a freezer of this brand sold ata certain store. Suppose that X has pmf x 16 18 20 p(x) 0.2 0.5 0.3 a. Compute E(X), E(X2), and V(X). b. If the price of a freezer having capacity X is70X - 650, what is the expected price paid by thenext customer to buy a freezer? c. What is the variance of the price paid by the nextcustomer? d. Suppose that although the rated capacity of a freezeris X, the actual capacity is h(X) = X - 0.008X2. Whatis the expected actual capacity of the freezer purchased by the next customer?
If a probability generating function of a random variable x is Px(s)=(1/3+2/3s)^6 determine E(x),var(2x) and pr(X>1)
If X and Y are Gaussian random variables then what is E[XY]?
For a discrete random variable X if : Points ) P ( X = x ) = 0.1x , x = 2 , 3 , 5 , then E ( X2 ) =