Exercise 3If we increase the number of replicates to 1000, then we will encounter a larger percentage of possible values for p at frequencies proportional totheir probabilities of occurrence. By plotting these replicates in a histogram, we can start to visualize the probability distribution of p. The codebelow provides an example with sample size n = 10. Alter the plot so that the color is red, the x-axis reads "Proportion of Heads", y-axis reads"Frequency", and the title (main) says "Distribution of Sample Proportions, n=10":Code Start Over1 values-c("H","T")2 phats-replicate(1000, sum(sample(values, 10, replace-TRUE)--"H")/10)3 hist(phots, xlab-"X label here",ylab-"y label here", main-"Put title here",col="orange")Exercise 4Besides plotting the distribution, we can also use simulations to estimate the expected value/mean or standard deviation of random variables.The output below computes the mean. Change it so that it computes the standard deviation (command=sd):CodeRun CodeStart Over1 volues-c("H","T")2 repeats-replicate(1000, sum(sample(values, 10, replace-TRUE)--"H")/10)3 mean(repeats)Run Code

Exercise 3 If we increase the number of replicates to 1000, then we will encounter a larger percentage of possible values for at frequencies proportional to their probabilities of occurrence. By plotting these replicates in a histogram, we can start to visualize the probability distribution of p. The code below provides an example with sample size = 10. Alter the plot so that the color is red, the x-axis reads "Proportion of Heads", y-axis reads "Frequency", and the title (main) says "Distribution of Sample Proportions, n=10": Code Start Over 1 volues-c("H","T") 2 phats-replicate(1000, sum(sample(values, 10, replace-TRUE)--"H")/10) 3 hist(phots, xlab-"X label here" ,ylab-"y label here", main-"Put title here",col-"orange") Run Code Exercise 4 Besides plotting the distribution, we can also use simulations to estimate the expected value/mean or standard deviation of random variables. The output below computes the mean. Change it so that it computes the standard deviation (command=> sd): Code Start Over 1 volues-c("H","T") 2 repeats-replicate(1000, sum(sample(values, 10, replace-TRUE)--"H")/10) 3 mean(repeats) Run Code

Exercise 3 If we increase the number of replicates to 1000, then we will encounter a larger percentage of possible values for at frequencies proportional to their probabilities of occurrence. By plotting these replicates in a histogram, we can start to visualize the probability distribution of p. The code below provides an example with sample size = 10. Alter the plot so that the color is red, the x-axis reads "Proportion of Heads", y-axis reads "Frequency", and the title (main) says "Distribution of Sample Proportions, n=10": Code Start Over 1 volues-c("H","T") 2 phats-replicate(1000, sum(sample(values, 10, replace-TRUE)--"H")/10) 3 hist(phots, xlab-"X label here" ,ylab-"y label here", main-"Put title here",col-"orange") Run Code Exercise 4 Besides plotting the distribution, we can also use simulations to estimate the expected value/mean or standard deviation of random variables. The output below computes the mean. Change it so that it computes the standard deviation (command=> sd): Code Start Over 1 volues-c("H","T") 2 repeats-replicate(1000, sum(sample(values, 10, replace-TRUE)--"H")/10) 3 mean(repeats) Run Code

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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please try to simulate the probability of rolling a Die with Sample Space* S={1,2,3,4,5,6} and the probability of each sample point has a 1/6 chance of occurring, i.e., you need to verify that your simulation converges to 1/6 when you select one point of sample space. When X is a random variable for sample point of rolling a Die, Pr(X<=4)=2/3. Please verify this result by simulation. Please let me know how to make an Excel file as stated above.
Pick one million sets of 12 uniform random numbers between 0 and 1. Sum up the 12 numbers in each set. Make a histogram with these one million sums, picking some reasonable binning. You will find that the mean is (obviously?) 12 times 0.5 = 6. Perhaps more surprising, you will find that the distribution of these sums looks very much Gaussian (a "Bell Curve"). This is an example of the "Central Limit Theorem", which says that the distribution of the sum of many random variables approaches the Gaussian distribution even when the individual variables are not gaussianly distributed. mean Superimpose on the histogram an appropriately normalized Gaussian distribution of 6 and standard deviation o = 1. (Look at the solutions from the week 5 discussion session for some help, if you need it). You will find that this Gaussian works pretty well. Not for credit but for thinking: why o = 1 in this case? (An explanation will come once the solutions are posted).
An Event In the context of the probability experiment just described. Consider the event in which the two numbers on the two dice add to 12. What is the size of this set? Probability of an event (1/2) What is the probability of the event just described? Write your answer as a fraction of integers. For example, if the answer were 17/20 then enter 17/20 with no spaces or other symbols. You may reduce the fraction by cancelling factors common to the numerator and denominator but you do not need to do this. Probability of an event (2/2) What is the probability that at least one 4 appears? Write your answer as a fraction of integers. For example, if the answer were 17/20 then enter 17/20 with no spaces or other symbols. You may reduce the fraction by cancelling factors common to the numerator and denominator but you do not need to do this.
We all know that when the temperature of a metal increases, it begins to expand. So, we experimented with exposing a metal rod to different temperatures and recorded its length as follows: 20 30 50 55 60 Temp Length 0.5 25 35 40 45 65 1.8 6.2 6.5 7.8 9.4 9.8 10.9 Required: 1. Implement and plot a simple linear regression for the above data, where the temperature is “x", and the length is “y"
We all know that when the temperature of a metal increases, it begins to expand. So, we experimented with exposing a metal rod to different temperatures and recorded its length as follows: 20 Length Temp 25 30 35 40 45 50 55 60 65 0.5 1.8 5 6.2 6.5 7.8 9.4 9.8 10.9 Required: 1. Implement and plot a simple linear regression for the above data, where the temperature is “x", and the length is "y" 2. Implement and plot a multiple linear regression "Polynomial regression" with different degrees. For example, Degree of 3: Y = w,x' + w2x? + W3x³ + W4 Where w4 represents bias. *you can use normal equation to calculate 'W' as follow: W (X".X)².(X".Y) Then calculate Y, Where Y = X.WT 3. Try degree of 2, 3, 5, and 8
The following table contains output from a lasso fit to a linear model with d = 5 variables and n = 50 observations. Starting from the left, the columns are X, and B₁,..., B5, i.e. each row has X and the transposed column vector (X). 0.00000 1.20706 -0.66487 0.46392 0.19746 -0.38526 6.18304 1.05715 -0.50740 0.27952 0.00000 -0.17280 12.48795 0.91734 -0.36985 0.11063 0.00000 0.00000 16.89171 0.82829 -0.28890 0.00000 0.00000 0.00000 33.19002 0.53551 0.00000 0.00000 0.00000 0.00000 59.28000 0.00000 0.00000 0.00000 0.00000 0.00000 For each of the required computations below, briefly report your procedure and the required quantity. a) For each row in the table, compute s, the proportion of shrinkage defined as s = s(X) = ||B(A)||₁/ maxx ||B(A)||1- b) Consider X'= 25.040865. Note that X' is the intermediate value between λ = 16.89171 and λ = 33.19002 of the 4th and 5th rows above. Using this value of X', compute and report the shrunk estimator B(x'). c) Give the proportion of shrinkage s(X')…
If we add a positive constant to each of the array of values, then the z-score of an observation will also rise. [T or F]. Explain the answer.
Generate 100 synthetic data points (x,y) as follows: x is uniform over [0,1]10 and y = P10 i=1 i ∗ xi + 0.1 ∗ N(0,1) where N(0,1) is the standard normal distribution. Implement full gradient descent and stochastic gradient descent, and test them on linear regression over the synthetic data points. Subject: Python Programming
A and B stand in a line at random with 10 other people. What is the probability that there are exactly 3 people between A and B?
You are given a N*N maze with a rat placed at maze[0][0]. Find whether any path exist that rat can follow to reach its destination i.e. maze[N-1][N-1]. Rat can move in any direction ( left, right, up and down).Value of every cell in the maze can either be 0 or 1. Cells with value 0 are blocked means rat cannot enter into those cells and those with value 1 are open.Input FormatLine 1: Integer NNext N Lines: Each line will contain ith row elements (separated by space)Output Format :The output line contains true if any path exists for the rat to reach its destination otherwise print false.Sample Input 1 :31 0 11 0 11 1 1Sample Output 1 :trueSample Input 2 :31 0 11 0 10 1 1Sample Output 2 : false Solution: //// public class Solution { public static boolean ratInAMaze(int maze[][]){ int n = maze.length; int path[][] = new int[n][n]; return solveMaze(maze, 0, 0, path); } public static boolean solveMaze(int[][] maze, int i, int j, int[][] path) {//…
There are N people numbered from 1 to N around a round table. Everyone has a different number in their hands between 1 and N. We start with the first person and count the number in his hand and ask the related person to leave the table. If the number in the card odd, we count clockwise. if it is even, we count counterclockwise. Ensure that all people leave the table. The first person to leave the table is the first person. In the sample scenario, the first integer value in the table_in.txt file indicates the number of people around the table, it is 5. The value of the card in the first person’s hand is written on the next line, it is 3. The value of the second person’s card is written on the next line, it is 1. In the table_out.txt file, print the order of people leaving the table. Sample scenario: table_in.txt 5 3 1 2 2 1 table_out.txt 1 4 2 3 5 Constraints N < 1,000,000 Do the solution in C/C++ with the Doubly Circular Linked List. Your codes should also be able to…
Solve this problem using python. The experiment consists of two independent tosses of a fair coin, let X be the number of heads obtained. Define the random variable, define its PMF and plot it. Use appropriate scipy.stats methods to compute the probability of observing at least one heads.