Answer:
Given that:
You repeatedly draw size-n samples from a r.v. that has
a
distribution where n is pretty big. It is known that this r.v. has
a mean of v and a variance of 2v. What is the expected value,
variance, and approximate distribution of the sample
mean?
The mean and standard deviation .
The sample mean is the same as the mean , v, and sample variance is 2v/n
The distribution is approximately N(v,2v/n)
** Please rate positive if the answer was useful
2. You repeatedly draw size-n samples from a r.v. that has a x2 distribution where n is pretty big. It is known that th...
Independent random samples X1, X2, . . . , Xn are from
exponential distribution with pdfs
, xi > 0, where λ is fixed but unknown. Let
. Here we have a relative large sample size n = 100.
(ii) Notice that the population mean here is µ = E(X1) = 1/λ ,
population variance σ^2 = Var(X1) = 1/λ^2 is unknown. Assume the
sample standard deviation s = 10, sample average
= 5, construct a 95% large-sample approximate confidence...
If selecting samples of size n≤30 from a population with a known mean and standard deviation, what requirement, if any, must be satisfied in order to assume that the distribution of the sample means is a normal distribution? A) The population must have a normal distribution. B) The population must have a mean of 1. C) The population must have a standard deviation of 1. D) None; the distribution of sample means will be approximately normal.
Let X1,X2, , Xn be a random sample from a normal distribution with a known mean μ (xi-A)2 and variance σ unknown. Let ơ-- Show that a (1-α) 100% confidence interval for σ2 is (nơ2/X2/2,n, nơ2A-a/2,n).
Let X1,X2, , Xn be a random sample from a normal distribution with a known mean μ (xi-A)2 and variance σ unknown. Let ơ-- Show that a (1-α) 100% confidence interval for σ2 is (nơ2/X2/2,n, nơ2A-a/2,n).
Part D: 1. Draw 500 random samples of size 8 from a random number generator from a standard normal distribution. Then increase the sample size to 32. Finally, increase the sample size to 128. Plot histograms of the sampling distributions of (i) the sample mean andi) the sample variance, for each of these three sample sizes. Now repeat your experiments for three samples drawn from another parametric distribution of your choice (e.g., a uniform distribution) Discuss the results of your...
7.5 Suppose you draw a random sample of size n from a normal distribution with unknown mean u and known standard deviation o and construct a 95% confidence interval for u. If you want to halve the margin of error, how much larger would the sample size have to be?
Let X1, X2, . . . , Xn be a random sample of size n from a normal population with mean µX and variance σ ^2 . Let Y1, Y2, . . . , Ym be a random sample of size m from a normal population with mean µY and variance σ ^2 . Also, assume that these two random samples are independent. It is desired to test the following hypotheses H0 : σX = σY versus H1 : σX...
suppose X1, X2 is a random sample of size n = 2 from a
population distribution.
i) compute P(X1=X2)
ii) what is the probability that the sample mean is less than
1.5?
T 0 1 2 P(x) 0.2 0.5 0.3
We have a random sample of size 17 from the normal distribution N(u,02) where u and o2 are unknown. The sample mean and variance are x = 4.7 and s2 = 5.76 (a) Compute an exact 95% confidence interval for the population mean u (b) Compute an approximate (i.e. using a normal approximation) 95% confidence interval for the population mean u (c) Compare your answers from part a and b. (d) Compute an exact 95% confidence interval for the population...
1. Three randomly selected households are surveyed. The numbers of people in the households are 3, 4 and 11. Assume that samples of size n=2 are randomly selected with replacement from the population of3, 4, and 11. Listed below are the nine different samples. Complete parts (a) through (c).3,3 3,4 3,11 4,3 4,4 4,11 11,3 11,4 11,11a. Find the variance of each of the nine samples, then summarize the sampling distribution of the variances in the format of a table...
List all possible samples of size n=3, with replacement, from the population (1,3,5). Calculate the mean of each sample. Construct a probability distribution of the sample means and compute the mean, variance, and standard deviation of the sample means and compare to the mean, variance, and standard deviation of the population.