Lab 4(a) - ProbabilityPart 1: Theoretical versus empirical probabilityObjective: The objective of this assignment is to compare the theoretical and empirical probabilities whenrolling two six-sided dice. This will be achieved by rolling two dice multiple times and recording theoutcomes, and then comparing the observed frequencies to the expected probabilities.Procedure for obtaining the theoretical probability:1. In the table below, write down the sample space (that is, all the possible outcomes) when 2 six-sided dice are rolled then summed. For example, the result pictured below is 8. This result hasbeen filled in everywhere it belongs within this table.1234563+5=8All possible outcomes when summing the result of rolling 2 six-sided dice1234563+5=85+3=82. Use the table above to help you compute the probability of obtaining a sum of 5 or a 6.P(5 U 6) = Lab 4(a) - ProbabilityPart 1: Theoretical versus empirical probabilityObjective: The objective of this assignment is to compare the theoretical and empirical probabilities whenrolling two six-sided dice. This will be achieved by rolling two dice multiple times and recording theoutcomes, and then comparing the observed frequencies to the expected probabilities.Procedure for obtaining the theoretical probability:1. In the table below, write down the sample space (that is, all the possible outcomes) when 2 six-sided dice are rolled then summed. For example, the result pictured below is 8. This result hasbeen filled in everywhere it belongs within this table.1234563+5=8All possible outcomes when summing the result of rolling 2 six-sided dice1234563+5=85+3=82. Use the table above to help you compute the probability of obtaining a sum of 5 or a 6.P(5 U 6) =

Analysis: 1. Does the theoretical probability match the empirical probability? Explain why this is or whether this poses a problem. 2. Fill in the blank: The Law of Large Numbers tells us that the empirical probability approaches the theoretical probability when 3. Explain how to change the Procedure for the Empirical Probability so that the empirical probability more closely resembles the theoretical probability. 4. Implement the change you proposed in the previous problem. Explain the results of this implementation below. (Include screenshots from StatCrunch.) Conclusion: In conclusion, this assignment demonstrates the difference between theoretical and empirical probabilities. Theoretical probabilities are calculated based on the number of ways an event can occur divided by the total number of possible outcomes. Empirical probabilities are calculated based on the number of times an event actually occurs. By comparing the two, we can see how closely the outcomes of an experiment match the expected probabilities.

Analysis: 1. Does the theoretical probability match the empirical probability? Explain why this is or whether this poses a problem. 2. Fill in the blank: The Law of Large Numbers tells us that the empirical probability approaches the theoretical probability when 3. Explain how to change the Procedure for the Empirical Probability so that the empirical probability more closely resembles the theoretical probability. 4. Implement the change you proposed in the previous problem. Explain the results of this implementation below. (Include screenshots from StatCrunch.) Conclusion: In conclusion, this assignment demonstrates the difference between theoretical and empirical probabilities. Theoretical probabilities are calculated based on the number of ways an event can occur divided by the total number of possible outcomes. Empirical probabilities are calculated based on the number of times an event actually occurs. By comparing the two, we can see how closely the outcomes of an experiment match the expected probabilities.

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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1. ABC inc. stock is currently selling for $30, one year from today the stock price can either increase by 20% or decrease by 15%. The probability of an increase in the stock price is equal to 0.3. The one-year risk-free rate is 5% What is the value of a European put that expires in one year with an exercise price of $24. 2. Graphically, show the value and the profit and loss of the following butterfly position: Long in a call with an exercise price of $30, short in 2 calls with an exercise price of $45, and long in a call with an exercise price of 60. All calls are written on the same stock and have the same maturity. 3. "Early exercise of an American option on a stock that does not pay any dividend is not optimal regardless of whether the option is a Call or a Put". True, False, or Uncertain. Explain.
Please answer only correct. ASAP
See photo for details...Need help with Part B
Just how accurate are the weather forecasts we hear every day? The table below compares the daily forecast with a city's actual weather for a year. Actual Weather Forecast Rain No rain Rain 34 56 No rain 4 271 What is the probability that there was no rain forecasted or rain actually happened?
PRACTICE ANOTHER Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are the auditor for a very large corporation. The revenue file contains millions of numbers in a large computer data bank. You draw a random sample of n = 225 numbers from this file and r = 85 have a first nonzero digit of 1. Let p represent the population proportion of all numbers in the computer file that have a leading digit of 1. What is the value of the sample test statistic? (Round your answer to two decimal places.) ANSWER IS NOT 2.57 Find the P-value of the test statistic. (Round your answer to four decimal places.) ANSWER IS NOT 0.0102
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Terminology
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Part 2) Five hundreds tickets are sold at $ 2 each for a smartphone valued at $ 1000. What is the expected value of the gain if you purchase one ticket?
Answers 0.025 0.975 0.611 0.389