Question: Prove Theorem 5.1. THEOREM 5.1 Let c be a constant, let Y be a continuous random variable, and let g1(Y), g2(Y), ..., gx(Y) be k

Prove Theorem 5.1.

THEOREM 5.1 Let c be a constant, let Y be a continuous

THEOREM 5.1 Let c be a constant, let Y be a continuous random variable, and let g1(Y), g2(Y), ..., gx(Y) be k functions of Y. Then, E(c) = c E(cY) = cE(Y) E[g (Y) + g2(Y) + + g(Y)] = E[g(Y)] + E[g2(Y)] ++ Elgx(Y)] %3D

Step by Step Solution

★★★★★

3.36 Rating (168 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

We will prove each part of the theorem separately Part 1 Ec c Since c is a constant the expe... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Statistics For Engineering And The Sciences Questions!

Prove Theorem 1 for a 2 Ã 2 stochastic matrix E by first writing it in the form where 0 ¤ a ¤ 1 and 0 ¤ b ¤ 1. E= 1-a 1-b

Prove Theorem 5.3.3. Prove that by applying Taylors theorem with remainder (see Exercise 13 in Sec. 4.2) to the function f(x) = log(1 + x) around x = 0. lim n log(+an)-ancn 0

Prove Theorem 2.2.4 on page 73. In Theorem 2.2.4 Suppose that A1, A2, and B are events such that Pr(A1 B) > 0. Then A1 and A2 are conditionally independent given B if and only if Pr(A2|A1 B) =...

ttth Suppose that the sequence of bags {Bn | n N} is recursively enumerated by the computable function e(n, x) = fn(x), [7 marks] Hence prove that the set of all recursive bags cannot be recursively...

You are expected to play the role of a reviewer/editor and recommend revisions to the article. Your grade on this assignment will be based mainly on the thoroughness and correctness of the revisions...

my economics assign Consider the following economy. There are two periods, 0 and 1, and a single consumption good. The economy is populated by two types of agents: nanciers (F) and entrepreneurs (E)....

In a Hopfield neural network configured as an associative memory, with all of its weights trained and fixed, what three possible behaviours may occur over time in configuration space as the net...

2. Let X,Y have independent standard Normal distribution. Let U = X + Y, V = X Y. a. Find the joint pdf of U. V using theorem T2. h. Prove that U. V have independent Normal distributions from the...

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

1 2.3 Definition of a Discrete Probability Function Definition: Let S be a discrete sample space from some experiment. A function P, defined on all events in S, is said to be a probability function...

Is it primary government or blended or discretely presented? The City of Winitville is the primary government. The Winitville Board of Education is included with the city for financial reporting...

Determine whether each of the compounds is the R or the S enantiomers.

Complete the statements in the order they appear, first one person responding and then the other.

An experiment was carried out to investigate the effect of species (factor A, with I = 4) and grade (factor B, with J = 3) on breaking strength of wood specimens. One observation was made for each...

The strength of concrete used in commercial construction tends to vary from one batch to another. Consequently, small test cylinders of concrete sampled from a batch are "cured" for periods up to...

For the data of Example 11.5, check the plausibility of assumptions by constructing a normal probability plot of the residuals and a plot of the residuals versus the predicted values, and comment on...

A small biotechnology research corporation has been experiencing losses for the first three years of its existence, and thus has a negative balance in retained earnings. The corporations stock price,...

Fabulous Fabricators needs to decide how to allocate space in its production facility this year. It is considering the following contracts: B a. What are the profitability indexes of the projects? b....

4 . Shares of ABC Ltd are currently traded at Rs . 1 7 7 0 . A call option with a strike price of 1 7 5 0 and expiring in 9 0 days is traded at Rs . 6 0 while a put with same strike price and...