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 p 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 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 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 p 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 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 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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Let Ax = {a,b,...,z,—}, |Ax| = 27, denote alpahabet of letters in English text where - represents the space character between words. Let Px = {P₁, P2,..., P27} denote the probability of letters. 1) Estimate pi, by parsing the text "All Systems Red' by Martha Wells. To do this you have to parse the letters in the book and form a character vector x = = [1, 2,..., TN] where N is the number of letters in the book. (Turn all uppercase letters into lowercases and ignore the characters that are not in Ax). You may use Matlab or Python. Then you can estimate p; by its frequency in the text #(x₁ = ai) N where #(i = a;) denotes the number of times ï¿ = a¿ in x. Pi = (1)
Let's revisit our first problem, where we want to set up a series of chess matches so we can rank six players in our class. As we did before, we will assume that everyone keeps their chess rating a private secret; however, when two players have a chess match, the person with the higher rating wins 100% of the time. But this time, we are only interested in identifying the BEST of these six players and the WORST of these six players. (We don't care about the relative ordering or ranking of the middle four players.) Your goal is to devise a comparison-based algorithm that is guaranteed to identify the player with the highest rating and the player with the lowest rating. Because you are very strong at Algorithm Design, you know how to do this in the most efficient way. Here are five statements. A. There exists an algorithm to solve this problem using 6 matches, but there does not exist an algorithm using only 5 matches. B. There exists an algorithm to solve this problem using 7 matches,…
Size of sample space A six-sided dice is rolled, a five-sided dice is rolled and a three-sided dice is rolled. Considering this as a probability experiment, what is the size of the sample space? An Event In the context of the probability experiment just described (a 6-sided, a 5-sided, and a 3-sided dice thrown): Consider the event in which two face- up numbers on the three dice add to 10. What is the size of this set? Save Reset
Consider the experiment where a penny is flipped, a quarter is flipped, and a 6-sided die is rolled. Let d be the number of possible outcomes of this experiment. What is the value of d? (Give your answer as a single integer with no words.) Let E be the event that both the penny and the quarter come up Tails, and the die comes up an odd number. If p(E) = , where d is your answer above, what is the value of x? Enter your answer as a single integer with no words:
Just answer LETTERS D,E,F dont forget to answer this part too!! ?x = ? =
6...
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.
There are 22 gloves in a drawer: 5 pairs of red gloves, 4 pairs of yellow, and 2 pairs of green. You select the gloves in the dark and can check them only after a selection has been made. What is the smallest number of gloves you need to select to have at least one matching pair in the best case? in the worst case?
program
Generate a probability histogram of the number of rolls required of two dice before a sum of “7” appears (graphical answer followed by Matlab code). Note: Don’t plot experiment that took more than 60 rolls.
Appendix A 10-Fold Cross Validation for Parameter Selection Cross Validation is the standard method for evaluation in empirical machine learning. It can also be used for parameter selection if we make sure to use the training set only. To select parameter A of algorithm A(X) over an enumerated range d E [A1,..., A] using dataset D, we do the following: 1. Split the data D into 10 disjoint folds. 2. For each value of A e (A1,..., Ar]: (a) For i = 1 to 10 Train A(A) on all folds but ith fold Test on ith fold and record the error on fold i (b) Compute the average performance of A on the 10 folds. 3. Pick the value of A with the best average performance Now, in the above, D only includes the training data and the parameter A is chosen without the knowledge of the test data. We then re-train on the entire train set D using the chosen A and evaluate the result on the test set.
We can specify the PageRank algorithm's convergence threshold using proc networks. This figure has to be positive. Default value is 1E-9. When the difference between the PageRank scores of the current iteration and the previous iteration is less than or equal to the tolerance set, the PageRank algorithm ceases iterating. We can use the PAGERANKTOLERANCE= parameter to specify the convergence tolerance. Write The example code demonstrates how to calculate PageRank centrality using a proc network built on a directed graph with unweighted links.