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1. A majority verdict of 10-2 or better may be permitted in a jury trial. Assuming each juror has probability 0.9 of reaching a Guilty verdict, and decides independently, what is the probability the jury decides to convict?
2. For both the Gamma and Beta distribution, find the value of x that maximizes the density function. When is there just one local maximum?
3. The Logarithmic distribution has been used in ecology to model how often any particular species appears in a habitat. Its pgf is of the form cln(1 - qz), where c is a constant and 0 < q < 1. Find c in terms of the parameter q, and write down the expression fo pk, the chance a species is located k times.(Partial solution provided in attachment)
4. Eleven horses enter a race. Mr C takes exactly 60 second to complete the course. Each of the other ten horses, independently, takes more than 60 seconds with probability p, or less than 60 seconds with probability 1 - p. Give a model for Mr C's position in the race. Find the chances that he wins, and he is placed (i.e. in the first three). Find the value of p that makes all eleven horses equally likely to win. For this value of p, find the chance Mr C is placed. Is it a surprise that your last answer is not 3/11?
The area of study is Sampling Methods and the Central Limit Theorem. Consider the digits in the phone numbers on a randomly selected page of your local phone book a population.
Suppose that you select a 50 families sample. Which is the form expected from the distribution of the average or median of the sample?
Based upon the following data, what is the expected value of perfect information, assuming the probability of the state of nature that favors location A occurring is 0.50, the probability of the state of nature that favors location B occurring is ..
suppose x and y are continuous random variables with joint pdf fx y 24xy 0 lt x 0 lt y and x y lt 1 and zero
Use the frequency chart on the age of actors and when they won a prestigious award and construct a corresponding histogram.
a researcher reported a correlation of 1.25 between an iq test and grades in epy 6214. which one of the following
Determine the mean, median, and range for each of two data sets. b. Determine standard deviation using rule of thumb for each of data sets.
audrey an astronomer is searching for extra-solar planets using the technique of relativistic lensing. though there are
the following are the numbers of defective parts produced in a shift by 10 workers before and after going through a
A study was conducted with alpha = 0.05 to determine if there is a significant linear correlation between the number of credit hours earned at the time of taking statistics 101 and the grade in the course. Eight pairs of data were collected.
Do these results suggest that the racial makeup of the faculty members is different from that of the students? (Use the .05 significance level.) Use the five steps of hypothesis testing and explain your findings.
Using symbols state hypotheses (H 0 and H 1 ) for two-tailed test. Sketch suitable distribution and locate critical region for a = 0.05.
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