Exercise 5.18.6: Calculating probabilities of independent events. A biased coin is flipped 10 times. In a single flip of the coin, the probability of heads is 1/3 and the probability of tails is 2/3. The outcomes of the coin flips are mutually independent. What is the probability of each event? (b) The first 5 flips come up heads. The last 5 flips come up tails. (c) The first flip comes up heads. The rest of the flips come up tails.

Exercise 5.18.6: Calculating probabilities of independent events. A biased coin is flipped 10 times. In a single flip of the coin, the probability of heads is 1/3 and the probability of tails is 2/3. The outcomes of the coin flips are mutually independent. What is the probability of each event? (b) The first 5 flips come up heads. The last 5 flips come up tails. (c) The first flip comes up heads. The rest of the flips come up tails.

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter10: Classes And Data Abstraction

Section: Chapter Questions

Problem 19PE

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PLEASE TYPE ONLY*** Exercise 5.16.4: The probability of an event under the uniform distribution - picking teams. 10 kids are randomly grouped into an A team with five kids and a B team with five kids. Each grouping is equally likely. (b) There are two kids in the group, Alex and his best friend Jose. What is the probability that Alex and Jose end up on the same team? (c) If the group consists of five girls and five boys, what is the probability that all the girls end up on the same team?
PLEASE TYPE ONLY**** Exercise 5.17.4: The probability of events - 5-card hands. A 5-card hand is dealt from a perfectly shuffled deck of playing cards. What is the probability of each of the following events? (a) The hand has at least one club. (b) The hand has at least two cards with the same rank. (c) The hand has exactly one club or exactly one spade. (d) The hand has at least one club or at least one spade.
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Loop invariants Consider the following code, assuming that i, x, y, and n are integers, with n > 0. • State a non-trivial loop invariant for variable x. • Prove the loop invariant. Be sure that the proof includes the final conditions after the loop has ended. Note: a correct proof of an incorrect invariant will still receive partial credit. • Give the final value of a in terms of n. Hint: is the pattern close to (e.g. off by one) from some other pattern you might recognize? Hint: you might need to include a condition for y somewhere within your proof. i = 0; x = 1; while in do y = x + 2; x=x*y; i = 1 + 1; After the loop, x = (the invariant goes here)
Find the error in the following argument: Theorem. All computer programs contain the same number of bugs. Proof. If we show that any set of n programs contains the same number of bugs, then we have proved the theorem. We argue by induction on n. If n=1 then in any set of 1 program, all the programs contain the same number of bugs, so the statement is true, in this case. Now suppose that for every set of programs containing less then n programs, all the programs have the same number of bugs. Let DD be a set of n programs p1,p2,…,pn. Now the set D1={p2,…,pn} contains n−1 programs and hence they all contain the same number of bugs, by the induction hypothesis. Similarly the set D2={p1,…,pn−1} contains n−1 programs and hence they all contain the same number of bugs. In particular p1 and pn contains the same number of bugs as the other programs in the set. Hence all the programs contain the same number of bugs.
[In C language] The concept of a "drunkard's walk" involves an individual who starts walking aimlessly from a lamp post. With each step they take, they move randomly either north, south, east, or west, each with a 25% probability. As the individual takes more steps, they tend to forget where they started and continue taking random steps. The objective is to determine how far the individual will be from the starting point (0,0) after taking N number of steps. To simulate this random walking motion for N steps, we can create a computer program. This program should ask the user to input an integer representing the number of steps to be taken. It should work for any positive value of steps, even for a large number. However, if the user enters an invalid number (such as a negative value), the program should display an error message. After each step, the program should show the current location of the random walker with respect to the origin (lamp post). Finally, when the random…
* When you throw a rock at some elevation part of its potential energy is converted to kinetic energy while another part is destroyed because of the hot surrounding False True * A pressure vessel can be treated as =thin-walled when the r/t 10 10 or greater 1 O is a point on stress-strain curve which indicates the limit of elastic behavior and the beginning of plastic behavior Yield point O Elastic point plastic point
Correct answer will be upvoted else Multiple Downvoted. Computer science. Athenaeus has recently wrapped up making his most recent melodic piece and will introduce it tomorrow to individuals of Athens. Tragically, the tune is somewhat dull and almost certain will not be met with a warm gathering. His tune comprises of n notes, which we will treat as certain integers. The variety of a tune is the number of various notes it contains. As a supporter of music, Euterpe looks after arrangers and guides them all through the method involved with making new tunes. She chose to help Athenaeus by changing his melody to make it more assorted. Being a minor goddess, she can't self-assertively change the tune. All things being equal, for every one of the n notes in the tune, she can either leave it for what it's worth or increment it by 1. Given the tune as an arrangement of integers portraying the notes, discover the maximal, attainable variety. Input The input comprises of numerous…
9. Let m, n are integers. Use a proof by contraposition to prove that if m*n is even, then m is even or n is even. 10. Let n be an integer. Use a proof by contradiction to prove that if 3n+2 is even, then n is even.
Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. Today the kindergarten has another gathering of n kids who should be situated during supper. The seats at the table are numbered from 1 to 4n. Two children can't sit on a similar seat. It is realized that two children who sit on seats with numbers an and b (a≠b) will enjoy if: gcd(a,b)=1 or, a partitions b or b separates a. gcd(a,b) — the greatest number x with the end goal that an is distinct by x and b is detachable by x. For instance, if n=3 and the children sit on seats with numbers 2, 3, 4, then, at that point, they will enjoy since 4 is isolated by 2 and gcd(2,3)=1. On the off chance that children sit on seats with numbers 4, 6, 10, they won't enjoy. The educator truly doesn't need the wreck at the table, so she needs to situate the children so there are no 2 of the child that can enjoy. All the more officially, she needs no pair of seats an and b that the children…
****GRADIENT DECENT-MACHINE LEARNING*** In measurements, straight relapse is a direct way to deal with demonstrate the connection between a reliant variable and at least one free factor. Let X be the autonomous variable and Y be the reliant variable. We will characterize a straight connection between these two factors as follows: Y = mX + c This is the condition for a line that you concentrated on in secondary school. m is the incline of the line and c is the y block. Today we will utilize this condition to prepare our model with a given dataset and anticipate the worth of Y for some random worth of X. Our test today is to decide the worth of m and c, with the end goal that the line relating to those values is the best fitting line or gives the base blunder. One method for tackling this issue is to utilize Gradient Decent (The reference here contain more subtleties of Gradient respectable and test code, attempt not use numpy in this inquiry): The Algorithm of slope good to find m…
Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. Two cells are adjoining in the event that they share a side. Thusly, every cell (x, y) has precisely three neighbors: (x+1, y) (x−1, y) (x+1, y−1) in case x is even and (x−1, y+1) in any case. At first a few cells are contaminated, all the others are sound. The course of recuperation starts. Each second, for precisely one cell (despite the fact that there may be different cells that could change its state) one of the accompanying occurs: A sound cell with something like 2 contaminated neighbors likewise becomes tainted. A contaminated cell with something like 2 solid neighbors likewise becomes sound. In the event that no such cell exists, the course of recuperation stops. Patient is considered recuperated if the course of recuperation has halted and every one of the cells are solid. We're keen on a most dire outcome imaginable: is it conceivable that the patient…