Already have an account? Get multiple benefits of using own account!
Login in your account..!
Remember me
Don't have an account? Create your account in less than a minutes,
Forgot password? how can I recover my password now!
Enter right registered email to receive password!
Question: A random variable is said to have the (standard) Cauchy distribution if its PDF is given by (5.2.6). This exercise uses computer simulations to demonstrate that a) samples from this distribution often have extreme outliers (a consequence of the heavy tails of the distribution), and (b) the sample mean is prone to the same type of outliers. (In fact, for any sample size, the sample mean has the standard Cauchy distribution, implying that the LLN and CLT do not apply for samples from a Cauchy distribution.)
(a) The R commands x=rcauchy(500); summary(x) generate a random sample of size 500 from the Cauchy distribution and display the sample's five number summary; see Section 1.7. Report the five number summary and the interquartile range, and comment on whether or not the smallest and largest order statistics are outliers. Repeat this 10 times.
(b) The R commands m=matrix(rcauchy(50000), nrow=500); xb=apply(m, 1, mean); summary(xb) generate the matrix m that has 500 rows, each of which is a sample of size n = 100 from the Cauchy distribution, compute the 500 sample means and store them in xb, and display the five number summary of xb. Repeat these commands 10 times, and report the 10 sets of five number summaries. Compare with the 10 sets of five number summaries from part (a), and comment on whether or not the distribution of the averages seems to be as prone to extreme outliers as that of the individual observations.
Determine the failure rate and the reliability. Find the probability that the machine operates for at least 12 hours before breaking down.
The vehicle speeds at a particular interstate location can be described by a normal curve. The mean speed is 67 mph, and the standard deviation is 6 mph.
a safety light is designed so that the times between flashes are normally distributed with a mean of 4.50 s and a
Calculate the exact percentage, within a randomly selected list, of neighbouring digits that would have the same value, and the percentage of neighbours whose value differs by 1 (and do NOT count 0 and 9 as differing by 1).
The leisure services committee of a local authority has seen its budget decline over the last few years and is currently having to consider closing a number.
an instructor believes that 20 or less of the students who finish a statistics course get an a grade. a sample of 90
What are the possible combinations of coins that Sanjay could have received in change?
one of larrys investments is going to mature and he wants to determine how to invest the proceeds of 30000. larry is
What is the correlation between Age Difference and Year?- Interpret the slope of this line.- Predict the average age difference in 2015.
That is, find the 80thpercentile, which is the X that represents the weight of the suitcase. Assume that the variable is normally distributed.
What's the probability the newspaper's sample will lead them to predict defeat? Be sure to verify that the assumptions and conditions necessary for your analysis are met.
Identify what you think is the best measure of variability to use for your example and explain why you believe it to be better than the others.
Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!
whatsapp: +1-415-670-9521
Phone: +1-415-670-9521
Email: [email protected]
All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd