Generate 1000 random numbers from a normal distribution with mean 1 and variance 2 using Box‐Muller...

Generate 1000 random numbers from a normal distribution with mean 1 and variance 2 using Box‐Muller transformation in R.

Expert Solution

R code

few samples shown below

milcah answered 1 year ago

Generate 1000 random numbers from ??2, 5? starting with standard normal random numbers in R.

Generate 1000 random numbers from ??3? starting with standard normal random numbers in R.

Assume that we draw random numbers from a normal distribution with mean μ = 5, variance...

Assume that we draw random numbers from a normal distribution with mean μ = 5, variance σ2 = 10. • (a) According to Central Limit Theorem what is the sample mean and SE when we have sample size of 10, 100, 1000 and 10000? • (b) Experimentally justify the Central Limit Theorem using simulation given sample a size of 10, 100 and 1000 (for each given sample size you can use 50000 simulations to explore the sampling distribution of the...

A computer was used to generate ten random numbers from a normal distribution with a set...

A computer was used to generate ten random numbers from a normal distribution with a set of unknown mean and variance: −1.1623, 0.2210, 1.6518, −1.1312, −0.2879, −1.0458, 1.3706, −0.7492, −0.1355, −1.2686. Eight more random normal numbers with the same variance perhaps a different mean were then generated (the mean may or may not actually be different): 0.3472, 2.2437, 1.0712, 2.5906, 0.5163, −1.1743, 0.0473, −0.8338. (a) What do you think the means of the random normal number generators were? What do...

Coding Language: R Generate 100 observations from the normal distribution with mean 3 and variance 1....

Coding Language: R Generate 100 observations from the normal distribution with mean 3 and variance 1. Compute the sample average, the standard error for the sample average, and the 95% confidence interval. Repeat the above two steps 1000 times. Report (a) the mean of the 1000 sample means, (b) the standard deviation of the 1000 sample means, (c) the mean of the 1000 standard errors, and (d) how many times (out of 1000) the 95% confidence intervals include the population...

The following numbers constitute a random sample from a normal distribution with an unknown mean and...

The following numbers constitute a random sample from a normal distribution with an unknown mean and unknown variance σ 2 1 : 15.0 19.1 16.6 20.4 13.5 (a) Test at the 5% significance level H0 : µ = 15 against Ha : µ > 15. Again, do the problem in two ways- first by obtaining the rejection region and second, by using the p-value. (b) Suppose we have another random sample from a normal distribution with an unknown mean and...

Let ?1,?2, ?3, … , ?25, be a random sample from a normal distribution having variance...

Let ?1,?2, ?3, … , ?25, be a random sample from a normal distribution having variance 100. a. Find the rejection region for a test at level ? = .1 of ?0: ? = 0 ?1: ? = 1.5 b. What is the power of the test?

a) Using the programming tool of your choice generate 10 random numbers from a flat distribution...

a) Using the programming tool of your choice generate 10 random numbers from a flat distribution between -0.5 and 0.5, and find the mean of these 10 numbers. Consider this mean to be the ‘result’ of this procedure. b) Repeat this 10 times and calculate the mean and variance of your 10 results. Is the distance of the mean from 0 about what you would expect? Why? c) Now repeat it 100 times and calculate the mean and variance. Is...

Use R and perform following: Generate 1000 observations from an exponential distribution with mean 10. Generate...

Use R and perform following: Generate 1000 observations from an exponential distribution with mean 10. Generate 1000 observations from a central t-distribution with 8 degree of freedom. Make a qqplot of observations in problem 1 versus quantiles generated from a t-distribution with 8 degree of freedom. Can the t distribution be used to approximate data in part 1?Submit the plot. Repeat above part but submit a qqplot of the observations in 1 versus quantiles from an exponential with mean 1....

Let X have Normal distribution with mean 45 and variance 81. If a random sample of...

Let X have Normal distribution with mean 45 and variance 81. If a random sample of size 25 is taken, which of the following is the probability that the sample average is between 41.40 and 45.63?

Question