4- A gambler plays roulette game and he is insisting to play all his money to black (A roulette wheel has38 slots: 18 are black, 18 are red, and 2 are green).a) Try to calculate required number of spin for average(µ) loss corresponds to the certain amount ofhis initial money (M) completely. Around this average loss, what is the confidence interval (95% oru±20 ) of the money (the variance (O? ) of the process should be calculated as well)?b)RV x is money (won (n times) or lost(N-n times) amount where N is number of spin, e.g. 25, 50,100, 200, 400, 500,..1500...) try to establish a distribution and all moments of this RV. Try to explainwhether his decision is sustainable or not. Try to find a winning strategy. Plot the probability densityfunction for various N values.

Name: 4- A gambler plays roulette game and he is insisting to play all his
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: 4- A gambler plays roulette game and he is insisting to play all his money to black (A roulette wheel has38 slots: 18 are black, 18 are red, and 2 are green).a) Try to calculate required number of spin for average(µ) loss corresponds to the certain

A roulette wheel has 38 slots: 18 are black, 18 are red, and 2 are green => The probability that…

Math

Probability

4- A gambler plays roulette game and he is insisting to play all his money to black (A roulette wheel has 38 slots: 18 are black, 18 are red, and 2 are green). a) Try to calculate required number of spin for average(µ) loss corresponds to the certain amount of his initial money (M) completely. Around this average loss, what is the confidence interval (95% or u±20 ) of the money (the variance (O² ) of the process should be calculated as well)? b)RV x is money (won (n times) or lost(N-n times) amount where N is number of spin, e.g. 25, 50, 100, 200, 400, 500,..1500...) try to establish a distribution and all moments of this RV. Try to explain whether his decision is sustainable or not. Try to find a winning strategy. Plot the probability density function for various N values.

4- A gambler plays roulette game and he is insisting to play all his money to black (A roulette wheel has 38 slots: 18 are black, 18 are red, and 2 are green). a) Try to calculate required number of spin for average(µ) loss corresponds to the certain amount of his initial money (M) completely. Around this average loss, what is the confidence interval (95% or u±20 ) of the money (the variance (O² ) of the process should be calculated as well)? b)RV x is money (won (n times) or lost(N-n times) amount where N is number of spin, e.g. 25, 50, 100, 200, 400, 500,..1500...) try to establish a distribution and all moments of this RV. Try to explain whether his decision is sustainable or not. Try to find a winning strategy. Plot the probability density function for various N values.

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...

See similar textbooks

Similar questions

A clinical trial for a psychological therapy for trauma takes 37 women and gives them one treatment for trauma and then, a year later, gives them a different treatment. The measure used to indicate success is a Likert scale where 5 means 'l found the treatment very helpful' and 1 means 'l didn't find it helpful at all. The lead researcher gathers the data and she finds a very high variance of scores across the women in each treatment, and considers giving up the analysis. She plans to do a difference in means analysis with unequal variances (she tested and found the variances were unequal). She asks for your advice: a. She is being too hasty because she is using the wrong technique. This is a paired sample and when she takes the difference in the Likert scale for each subject across the two treatments the variance of the remaining lifferences might be so low that she can detect which treatment is statistically better b. She cannot give different treatments to the same people - it…
Over the years, a sushi restaurant has had a mean customer satisfaction rating of 72.5 with a variance of 24.7. The owner has hired you to perform a hypothesis test to see if using a new menu will have any effect on the variance, o“. To do so, you survey a random sample of 19 customers who ordered from the new menu. For the customers surveyed, the variance of ratings is 44.3. Under the assumption that the customer ratings using the new menu follow a normal distribution, you will perform a chi-square test. Find x, the value of the test statistic for your chi-square test. Round your answer to three or more decimal places.
Two groups of mice were injected with a measured amount of tumor pulp. The first group of 27 mice was given a high dosage of chemotherapy while the second group of 30 mice was given a low dosage of chemotherapy. After forty days, the first group had an average tumor size of 0.51cc with a variance of 0.10; the second group had an average tumor size of 0.64cc with a variance of 0.045. Were the tumor sizes of group 1 significantly smaller than those of group 2? What is the observed test statistic?
The average age at which adolescent girls reach their adult height is 16 years. Suppose you have a sample of 29 adolescent girls who are developmentally delayed, and who have an average age at which they reached their adult height of 17.8 years and a sample variance of 77.4 years. You want to test the hypothesis that adolescent girls who are developmentally delayed have a different age at which they reached their adult height than all adolescent girls. In order to calculate the t statistic, you first need to calculate the estimated standard error. The estimated standard error SM = (round to four decimals)
The reaction time in a chemical process (in seconds) is normally distributed with a mean of 2.94 and variance of 0.68.(a) What is the probability that the reaction time is exactly 2.94 seconds?(b) What is the probability that the reaction time is at least three seconds, given that it is less than 3.5 seconds?
Suppose we have two SRSS from two distinct populations and the samples are independent. We measure the same variable for both samples. Suppose both populations of the values of these variables are normally distributed but the means and standard deviations are unknown. For purposes of comparing the two means, we use (a) Two-sample t procedures (b) Matched pairs t procedures (c) z procedures (d) The least-squares regression line (e) None of the above. The answer is
A study was conducted that measured the total brain volume (TBV) (in mm³) of patients that had schizophrenia and patients that are considered normal. The first table contains the TBV of the non- schizophrenic patients and the second table contains the TBV of schizophrenia patients. Compute a 99% confidence interval for the difference in TBV of non-schizophrenic patients and patients with Schizophrenia. Prior studies say nothing about the equality of variances. Round to the nearest whole number. Total Brain Volume (in mm³) of Non-Schizophrenic Patients 1487997 1611227 1527495 1409812 1297379 1400278 1724615 1249097 1309037 1546157 1352710 1620645 1446958 1540957 1535216 1303042 1363737 1318121 1460479 1602502 1353583 1292976 1558222 1474289 1541397 1373993 1398046 1282528 1516312 1567897 1532468 1381812 Total Brain Volume (in mm³) of Schizophrenia Patients 1653156 1037545 1063003 1287704 1262253 1455977 1438274 1280706 1451005 1283081 1214368 1536994 1082431 1372061 1096716 1699683…
The average age at which adolescent girls reach their adult height is 16 years. Suppose you have a sample of 29 adolescent girls who are developmentally delayed, and who have an average age at which they reached their adult height of 17.8 years and a sample variance of 77.4 years. You want to test the hypothesis that adolescent girls who are developmentally delayed have a different age at which they reached their adult height than all adolescent girls. In order to calculate the t statistic, you first need to calculate the estimated standard error. The estimated standard error SM= (round to four decimals)
Deal with it.I need the correct answer
A study was conducted to compare the length of time between men and women to assemble a certain product. Sample standard deviation in a random sample of times for 11 men was 8.6 minutes, and sample standard deviation in a random sample of times for 13 women was 6.9 minutes. Past experience indicate that population of times is normal for both men and women. Is it sufficient sample evidence to conclude that the variance of the lengths of time for men is larger than the variance of the lengths of time for women? Test appropriate hypothesis at a = 0.05 level of significance using critical value approach. Use S²/S2 as test statistic. Construct a 90% confidence interval for the ratio of two population variances. a. State null and research hypotheses H: H₁ b. The observed value of test statistic is c. State the rejection region d. Insert the word sufficient or insufficient into the following statement. There is of time for men is larger than the variance of the lengths of time for women.…
The blood pressure and weight of Jellystone Park bears are correlated and .5 is the correlation coefficient of blood pressure with weight. The average blood pressure is 150 with variance 36, for Jellystone Park bears. For a randomly selected bear with average weight if we predict its blood pressure is 150 after weighing it, using SLR, what is our expected squared error?