Consider a random sample of size one (n = 1) from the population of X with probability density function 2(0-²), if 0
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- Q5 Find the variance for the PDF px(x) = e-«/2, x > 0.Please help me for Question 2A random sample of 15 items is drawn from a population whose standard deviation is unknown The sample mean is = 760 and the sample standard deviation isS=20 Use Appendix D to find the values of Student's A (a) Construct an interval estimate of u with 99% confidence. (Round your answers to 3 decimal places.) The 99% confidence interval is from to (b) Construct an interval estimate of u with 99% confidence, assuming that s=40 (Round your answers to 3 decimal places.) The 99% cofidence interval is from to (c) Construct an interval estimate of u with 99% confidence assuming that s=8O (Round your answers to3 decimal places.) The 99% confidence interval is from
- Anomal distribution has of mu = 50 with sigma = 6 6. one score randomly selected from this distributionwhich is the probability that the score will be greater than X = 46SAT scores in one state is normally distributed with a mean of 1532 and a standard deviation of 200. Suppose we randomly pick 50 SAT scores from that state. a) Find the probability that one of the scores in the sample is less than 1492. P(X < 1492) = b) Find the probability that the average of the scores for the sample of 50 scores is less than 1492. P(X < 1492) =Obtain 100 (1 x)% confidence limits (for large samples) for the parameter 2 of the f(x, 2) = e-^.^* ; x ; x = 0, 1, 2,... x! Poisson distribution:
- Assume the random variable x is normally distributed with mean μ = 50 and standard deviation o = 7. Find the indicated probability. P(x > 35) P(x > 35)= (Round to four decimal places as needed.) ***The National Health and Nutrition Examination Survey reported in the recent year, the mean cholesterol level for U.S. adults was 202 with standard deviation of 41 (unit: mg/dl) A simple random sample of 110 adults are chosen. Let x¯ be the sample mean cholesterol with a) The probability that the sample mean cholesterol level of the sample of 110 is greater than 210 is P(x¯>210) = ["", "", "", ""] b) What is the probability that the sample mean is between 190 and 200: P(190<x¯<200) = ["", "", "", ""]Let X is a random variable with a pdf with mean u and standard deviation o (we do not know the actual shape of the pdf). If we draw reasonably large (n) samples from X, and calculate the sample mean X-bar, then what will be the pdf of the X-bar and WHY? |(Do not forget to mention the parameters of the pdf of X-bar) Answer here--->
- derive maximum likelihood estimator(s) of the underlying parameter(s) *In detailedLet X1,., X, be iid from Normal(e,0) population (0>0). Use the pivotal quantity to find (1-a) Confidence Interval for 0. ...Data taken from a sample of 25 LED lamps, a sample average of 2 years was obtained and a standard deviation of s=0.4 years. The estimator of the mean of lifetime of LED lamps at the confidence level/coefficient (1-α) is (2 ± 0.05 talpha/2 , where talpha/2 is the value of t in the t distribution with v=24) (2 ± 0.10 talpha/2 , where talpha/2 is the value of t in the t distribution with v=24) (2 ± 0.08 talpha/2 , where talpha/2 is the value of t in the t distribution with v=24 (other)