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A continuous-time signal x 0 (t) is band limited to 5 kHz, i.e., x 0 (t) has a spectrum X a(I) that is zero for |f| > 5 kHz. Only 10 seconds of the signal has been recorded and is available for processing. We would like to estimate the power spectrum of xa(t) using the available data in a radix-2 FFT algorithm, and it is required that the estimate have a resolution of at least 10 Hz. Suppose that we use Bartlett's method of periodogram averaging.
(a) If the data is sampled at the Nyquist rate, what is the minimum section length that you may use to get the desired resolution?
(b) Using the minimum section length determined in part (a), with 10 seconds of data, how many sections are available for averaging?
(c) How does your choice of the sampling rate affect the resolution and variance of your estimate? Are there any benefits to sampling above the Nyquist rate?
At the 0.10 level of significance, test the null hypothesis that the population variances are equal. Would your conclusion be different if the test had been conducted at the 0.05 level? At the 0.02 level?
RELIABILITY OF MEDICAL TESTS. Suppose 20% of the people who were referred to a clinic for the test did in fact have the disease. If the tes
Suppose a random sample of 5 observations on x yields data 1, .8, 1.3, 1.6, 2. What is the maximum likelihood estimate for ??
Researchers designed a questionnaire to identify compulsive buyers. For a sample of consumers who identified themselves as compulsive buyers, scores have a mean of 0.83 and a standard deviation of 0.24.
Determine and interpret the p-value for the test. Source: John Diamond, "Some Veterans Suffer Bone, Muscle Ailments," The Indiana Gazette, January 22, 1997, p. 5.
Another quote in the article is In response to the influenza vaccine, the meditators displayed a significantly greater rise in antibody titers.
There is significant evidence, alpha =0.05, to show that there is a difference in the proportions of patients who show improvement between treatments 1 and 2
At a certain stage in a trial, the judge feels the odds are two to one the defendent is guilty. It is determined that the defendent is left handed.
Modify the program again to print out, every 100 times, both of the following quantities: the proportion of heads minus 1/2, and the number of heads minus half the number of tosses. Do these numbers appear to approach 0 as n increases?
The probability of error in the transmission of a binary digit over a communication [2] channel is 1=103. Write an expression for the exact probability of more than 3 errors when transmitting a block of 103 bits. What is its approximate value? Ass..
At Ajax Spring Water, a half-liter bottle of soft drink is supposed to contain a mean of 540 ml. The filling process follows a normal distribution with a known process standard deviation of 4 ml. A sample of 36 bottles shows a mean fill of 538 ml...
What are your thoughts on websites that can help a person self-diagnose a problem that they are having? What can healthcare administrators do to help prevent their patients from self-diagnosing online? Please provide a response that is 250 words?
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