Question: Prove that, for any structure function , (x) = xi(1i, x) + (1 xi)(0i, x) where (1i, x) = (x1,..., xi1, 1, xi+1,..., xn),

Prove that, for any structure function φ,

φ(x) = xiφ(1i, x) + (1 − xi)φ(0i, x)

where

(1i, x) = (x1,..., xi−1, 1, xi+1,..., xn),

(0i, x) = (x1,..., xi−1, 0, xi+1,..., xn)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
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 Theory Of Probability Questions!

Q:

1. Prove that, for any structure function , (x) = xi(1i , x) + (1 xi)(0i , x) where (1i , x) = (x1, . . . , xi1, 1, xi+1, . . . , xn), (0i , x) = (x1, . . . , xi1, 0, xi+1, . . . , xn)

Q:

Prove that, for any structure function , (x) = xi(1i , x)+(1 xi)(0i , x) where (1i , x) = (x1, . . . , xi1, 1, xi+1, . . . , xn), (0i , x) = (x1, . . . , xi1, 0, xi+1, . . . , xn)

Q:

Describe, in detail, how the heapsort algorithm works. [10 marks] Show that the worst-case cost of heapsort is O(n log n). [6 marks] Would it be possible to implement a variant of heapsort based on a...

Q:

(a) In SystemVerilog, what is the difference between: (i) The ternary operator ? and if...then...else statements? [2 marks] (ii) always_ff and always_comb? [2 marks] (iii) Blocking, non-blocking and...

Q:

s1 educated (SSE) student for every three public school educated (PSE) students. Reasoning that students are not very dissimilar from threads, he suggests the following entry and exit routines be...

Q:

dee complete please help Complexity Theory (a) Defifine the set of Boolean expressions 2CNF and the language 2SAT over them. (b) For a Boolean expression in 2CNF, let G() be the directed graph with...

Q:

(Q1) Let A be an nn matrix with real entries and distinct eigenvalues. There are a few ways to measure the condition of A. In general, the condition number is given by (A) = ||A|| ||A1 ||. It...

Q:

This question concerns lexical grammars. (a) Tree Adjoining Grammars contain two types of elementary tree. (i) What are these trees called? [1 mark] (ii) If one were building a grammar for English...

Q:

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

Q:

Least Squares Approximation Hector D. Ceniceros 1 Least Squares Approximation Let f be a continuous function on [a, b]. We would like to find the best approximation to f by a polynomial of degree at...

Q:

One might think that performing a mammogram once each yearas opposed to once every three yearswould triple the cost per life saved. But according to Table, performing the exam annually raises the...

Q:

Comparison of Different Types of Accounting by Lessee and Lessor Part 1 Capital leases and operating leases are the two classifications of leases described in FASB pronouncements from the standpoint...

Q:

The Redmond Corporation has purchased a new piece of factory equipment on June 1 , 2 0 2 5 , and wishes to compare three depreciation methods: straight - line, double - declining - balance, and units...

Q:

The lack of innovation and entrepreneurial focus at American Express (AmEx) may be because of hubris, inertia, and a lack of capability. The firms performance in 2014 was not, by any means, what...

Q:

*26. Let denote the long run proportion of time a given Markov chain is in state /. (a) Explain why , is also the proportion of transitions that are into state / as well as being the proportion of...

Q:

25. Consider a Markov chain with states 0, 1,2, 3, 4. Suppose P04 = 1; and suppose that when the chain is in state /, / > 0, the next state is equally likely to be any of the states 0 , 1 , . . . , /...

Q:

24. A professor continually gives exams to her students. She can give three possible types of exams, and her class is graded as either having done well or badly. Let pt denote the probability that...

Q:

Explain, completely in your own words, what Marx meant by saying that a worker is "alienated from his product." Remember that the guideline for essay answers is five sentences. This answer will have...

Q:

Ayayal Inc's manufacturing overhead budget for the first quarter of 2022 contained the following data. Variable Costs Fixed Costs Indirect materials $14,880 Supervisory salaries $44,640 Indirect...

Q:

Total Variable Costs: $ Contribution Margin: $ Operating Income: $ b) If the company sells according to their estimates, what is the degree of operating leverage? The break-even point (in units)?...