The support functions For the next few questions, we'll be working on finding the roots for the following quadratic equation: f(x)=x²-1.5 which has the derivative: f'(x)=2r Before we get started on the root-finding, however, you are to write two functions that will come in handy later: f(x), which takes a number or numpy arrayx and returns f(x) as defined above. f_prine(x), which takes a number or numpy arrayx and returns f'(x) as defined above. Paste these two functions into the answer box below. Note: Each function can easily be written using just a return statement. If you're doing more than this, you're probably overthinking it. For example: Test print(f(x)) print(f_prine(x@)) Result 2.5 4

The support functions For the next few questions, we'll be working on finding the roots for the following quadratic equation: f(x)=x²-1.5 which has the derivative: f'(x)=2r Before we get started on the root-finding, however, you are to write two functions that will come in handy later: f(x), which takes a number or numpy arrayx and returns f(x) as defined above. f_prine(x), which takes a number or numpy arrayx and returns f'(x) as defined above. Paste these two functions into the answer box below. Note: Each function can easily be written using just a return statement. If you're doing more than this, you're probably overthinking it. For example: Test print(f(x)) print(f_prine(x@)) Result 2.5 4

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Solve both parts of the following question using R. Show the R code as well.
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In Python, write a function that produces plots of statistical power versus sample size for simple linear regression. The function should be of the form LinRegPower(N,B,A,sd,nrep), where N is a vector/list of sample sizes, B is the true slope, A is the true intercept, sd is the true standard deviation of the residuals, and nrep is the number of simulation replicates. The function should conduct simulations and then produce a plot of statistical power versus the sample sizes in N for the hypothesis test of whether the slope is different than zero. B and A can be vectors/lists of equal length. In this case, the plot should have separate lines for each pair of A and B values (A[1] with B[1], A[2] with B[2], etc). The function should produce an informative error message if A and B are not the same length. It should also give an informative error message if N only has a single value. Demonstrate your function with some sample plots. Find some cases where power varies from close to zero to…
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Without importing any Lib: