need help with foundation of statistics assignment due at midnight. includes Rstudio. Fairly textbook problems. Please let me know.

Question 1 (20 pts)

Random variable X follows a normal distribution: X = N(2,42), that is, µ = 2,‡ = 4

(a) (10 pts) Calculate the probability P(|X| Æ 3). Note: be careful, it is |X|. Use two methods to work on it below.

Method 1 (Theory): Using the transformation of general normal distribution to standard normal distribution method, finally use R code to calcuate it.

Method 2 (Simulation): Using simulation method (rnorm function) to estimate. Write down your R code and final result.

(b) (5 pts) Find the value k such that P(X k) = 0.2 (using the transformation of standard normal distribution method), and finally use R code to calculate it.

(c) (5 pts) Use simulation method to estimate the mean: E(e?X2).

Question 2 (20 pts)

Random variable T describes the life time of a laptop, which follows Exponential distribution. That is, T = Exp(—), where — = 6 (years).

(a) (10 pts) If a company bought 90 laptops of same type, find the probability that at least 43 laptops are still working at the end of 9 years? Also, what is the mean number of laptops that are still working at the end of 9 years in this company?

(b) (10 pts) Use simulation method to estimate the probability P(3 T 10) and the mean E(T3).

Write down your R code and final results.

Question 3 (20 pts)

Let X be a random variable with a density function (pdf)

f(x) = ce?x/2,x 0 (a) Calculate the value of c to make f(x) a valid pdf.

(b) Calculate the probability P(X Æ 6|X 3)

Question 4 (40 pts)

(a, 20 pts) In an exam, there are 100 questions of same di culty levels, and assuming the time to answer these questions are independent random variables. Also, the time to answer each questions follow the same distribution with the same mean µ = 35 seconds, and standard deviation ‡ = 15 seconds. Question: what is the probability that you can answer all the 100 questions within 1 hour? Finally you should use R code of standard normal distribution to calculate the final value.

(b, 20 pts) In a year, the mean SAT Math score for the female students is 518, standard deviation is 15; while the mean SAT Math score for the male students is 525, standard deviation is 25. If we randomly draw 100 females and 100 males from all the students who took the test. Calculate the probability that the male students’ average score are at least 10 points higher than female students’ average score. Finally you should use R code of standard normal distribution to calculate the final value.

Question 1 (20 pts)

Random variable X follows a normal distribution: X = N(2,42), that is, µ = 2,‡ = 4

(a) (10 pts) Calculate the probability P(|X| Æ 3). Note: be careful, it is |X|. Use two methods to work on it below.

Method 1 (Theory): Using the transformation of general normal distribution to standard normal distribution method, finally use R code to calcuate it.

Method 2 (Simulation): Using simulation method (rnorm function) to estimate. Write down your R code and final result.

(b) (5 pts) Find the value k such that P(X k) = 0.2 (using the transformation of standard normal distribution method), and finally use R code to calculate it.

(c) (5 pts) Use simulation method to estimate the mean: E(e?X2).

Question 2 (20 pts)

Random variable T describes the life time of a laptop, which follows Exponential distribution. That is, T = Exp(—), where — = 6 (years).

(a) (10 pts) If a company bought 90 laptops of same type, find the probability that at least 43 laptops are still working at the end of 9 years? Also, what is the mean number of laptops that are still working at the end of 9 years in this company?

(b) (10 pts) Use simulation method to estimate the probability P(3 T 10) and the mean E(T3).

Write down your R code and final results.

Question 3 (20 pts)

Let X be a random variable with a density function (pdf)

f(x) = ce?x/2,x 0 (a) Calculate the value of c to make f(x) a valid pdf.

(b) Calculate the probability P(X Æ 6|X 3)

Question 4 (40 pts)

(a, 20 pts) In an exam, there are 100 questions of same di culty levels, and assuming the time to answer these questions are independent random variables. Also, the time to answer each questions follow the same distribution with the same mean µ = 35 seconds, and standard deviation ‡ = 15 seconds. Question: what is the probability that you can answer all the 100 questions within 1 hour? Finally you should use R code of standard normal distribution to calculate the final value.

(b, 20 pts) In a year, the mean SAT Math score for the female students is 518, standard deviation is 15; while the mean SAT Math score for the male students is 525, standard deviation is 25. If we randomly draw 100 females and 100 males from all the students who took the test. Calculate the probability that the male students’ average score are at least 10 points higher than female students’ average score. Finally you should use R code of standard normal distribution to calculate the final value.

Presidential Communications Operations OfficePresidential News DeskSPEECH OF PRESIDENT RODRIGO ROA DUTERTE DURING THE RECOGNITION OF THE2019 SOUTHEAST ASIAN GAMES MEDALISTS[Delivered at the Rizal Hall,...QUESTION ONE: (35Points) Also complete a reconciliation.Mr. Madoff decides to form an animal shelter for dogs and cats. On May 1, (the Happiest day in my mom's life), he made the following transactions:1....i need a marketing assignment asap as I was let down by aother company. The assignment is a UK SME company to expand to China. The assignment should not be more that 3500 words. please include graphs etcMKT744...Programme Title: Honours Bachelor of Arts in Contemporary Disability StudiesAcademic Year: 2019/20ASSESSMENT GUIDELINESModule Title: Current Issues in Social CareLearner Group Code: L8MBACDS20OCASSESSMENT...Assessment 3• Type: Individual assessment, A Report• Word Limit - 2000 + -10% words not including a cover page, reference and appendix• Value: 20%• Due Date: 5.00pm Friday, Week 10Task Details (see the...Assessment 2 templateWord count of the template = approx. 750 wordsTool for critiquing QUALITATIVE research (1500 word-equivalent)Tool for critiquing qualitative research is modified based on the Critical...Assessment 3: Case StudyDue date: Week 10Group/individual: IndividualWord count/Time provided: 2000 wordsWeighting: 40%Unit Learning Outcomes: ULO-1, ULO-2, ULO-3, ULO-4 and ULO-5Assessment 3 DetailAnswer...**Show All Questions**