Python Programming: An Introduction to Computer Science
Python Programming: An Introduction to Computer Science
3rd Edition
ISBN: 9781590282779
Author: John Zelle
Publisher: Franklin Beedle & Associates
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Chapter 6, Problem 1D

Explanation of Solution

The two motivations for defining functions in your programs are: 

  • Reusability
  • Abstraction

The first motivation is reusability:

  • Once defined, a function can be used over and over and over again.
  • User can save your work by invoking the same function many times in the program.
  • Another aspect of reusability is that a single function can be used in several different and separate programs.
  • When a user needs to write a new program, user can go back to your old programs, find the functions he/she needs, and reuse those functions in his/her new program.
  • User can also reuse functions that somebody else has written...

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Can you help me solve this problem using Master's Theorem:Solve the recurrence relation f(n) = 3af(n/a) + (n + a)2 with f(1) = 1 and a > 1 byfinding an expression for f(n) in big-Oh notation.
here is example 7.6## Example 7.6 Suppose the sample population is χ 2 (2), which is non-normal but with same variance 4. ▶ Repeat the simulation, but replacing the N(0, 4) samples with χ 2 (2) samples. ▶ Calculate the empirical confidence level.(Empirical confidence level) n <- 20 alpha <- 0.05 UCL <- replicate(1000, expr = { x <- rchisq(n,df=2) (n-1)*var(x)/qchisq(alpha,df=n-1) }) sum(UCL >4) mean(UCL > 4) ## t.test function n <- 20 x <- rnorm(n,mean=2) result <- t.test(x,mu=1) result$statistic result$parameter result$p.value result$conf.int result$estimate
using r language
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