Use the OptimalBST algorithm to determine the cost and structure of an optimalbinary search tree for a set of n = 4 keys with the following probabilities:keyprobabilityA B C D0.1 0.5 0.3 0.1

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Answered: Use the OptimalBST algorithm to…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Please explain step by step each part in discrete math problem, thanks.
The Infinite Monkey Theorem states that a monkey hitting keys completely at random on a typewriter for an infinite amount of time will, eventually, type any given text. Even the complete works of William Shakespeare. Some quotes are truly amazing. Consider the famous quote, "NOT TODAY" --Arya Stark That's 9 amazing characters. Suppose a monkey is seated in front of a KEYBOARD WITH 28 CHARACTERS (one for each of the 26 letters in the alphabet, plus the space bar, and a comma). Suppose the monkey types only 9 characters completely at random. If X is the number of different 9 character strings it could have typed, then the chances that it typed the quote is one divided by X. What is X?
Cc.33.
a) Describe the linear congruential method for Random number generation. Using the multiplicative congruential method, generate a sequence of five- three-digit random integers with seed = 117 constant multiplier = 43 and modulus = 1000
Use the double hashing procedure we have described with p = 4969 to assign memory locations to files for employees with social security numbers k1 = 132489971, k2 = 509496993, k3 = 546332190, k4 = 034367980, k5 = 047900151, k6 = 329938157, k7 = 212228844, k8 = 325510778, k9 = 353354519, k10 = 053708912.
Example 7: Use a tree diagram to find the possible three-digit numbers than can be written using only the digits 1, 2, and 3. Assume repeated digits are NOT allowed. [Note: This process will be referred to as "without replacement".] Part I: Part II: Part III: Select the first digit Select the second digit Select the third digit
Data were collected from a random sample of 330 home sales from a community in 2003. Let Price denote the selling price (in $1,000), BDR denote the number of bedrooms, Bath denote the number of bathrooms, Hsize denote the size of the house (in square feet), Lsize denote the lot size (in square feet), Age denote the age of the house (in years), and Poor denote a binary variable that is equal to 1 if the condition of the house is reported as "poor." An estimated regression yields Price=129.9 +0.529BDR+25.5Bath +0.170Hsize +0.004Lsize +0.098Age-53.2Poor, R² = 0.78, SER=45.2. Suppose that a homeowner converts part of an existing family room in her house into a new bathroom. What is the expected increase in the value of the house? The expected increase in the value of the house is $. (Round your response to the nearest dollar.) Suppose that a homeowner adds a new bathroom to her house, which increases the size of the house by 109 square feet. What is the expected increase in the value of…
Let arr86 be a binary variable equal to 1 if a man was arrested during 1986, and zerootherwise. You have a dataset of young men from California who were born in 1960 or1961 and have at least one arrest prior to 1986. You also have data on the proportion ofprior arrests that led to a conviction (pcnv), the average sentence served from priorconvictions in months (avgsen), months spent in prison since age 18 prior to 1986(tottime), months spent in prison in 1986 (ptime86), and the number of quarters (0 to 4)that the man was legally employed in 1986 (qemp86). You estimate the following linearprobability model (standard errors are in parentheses): arr86 = 0.441 - .162pcnv + .0061avgsen - .0023tottime(.017) (.021) (.0065) (.005) - .022ptime86 - .043qemp86(.005) (.005) n= 2725R2=.0474 a) Interpret the coefficient on avgsen, commenting on both magnitude and significance. Based on these results, do longer sentences deter future crime? b) What is the predicted probability of arrest for a man…
6. A researcher develop one new prediction algorithm. He want to find out whether hisalgorithm predict a situation faster than the current method. He test his algorithm to makea prediction base on 4 sets of data. He recorded the computation time in microsecond andcompare it with current method and standard method. Table 5 give the computation timefor all method tested.TABLE 5Proposed Method Current Method Standard Method10 11 1313 16 177 9 915 16 19At 2.5% significance level, will you conclude that the computation time taken to predict is thedifferent for each of the three algorithms.
There are exactly 365 students taking Algorithms this semester. Assume that each of these students is equally likely to be born on any of the 365 days of the year. For this problem, let’s assume that no one is born on February 29. Determine the probability that at most one student is born on June 15.
1
Many online portals now use 2-Factor Authentication. After you login with your username and password, a code is sent to your phone and you have to enter this code. Assume this code is six digits long. What is the likelihood that this code will consist of at least one repeated digit? (zero is a valid digit, meaning an authentication code could consist of all zeroes. Here are examples of authentication codes with repeated digits – 000000, 154443, 112339, 556688). Please show how you would do this in excel, thank you!

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Use the OptimalBST algorithm to determine the cost and structure of an optimal binary search tree for a set of n = 4 keys with the following probabilities : key probability A B с D 0.1 0.5 0.3 0.1