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1. (a) Let X1,..., Xn be a random sample from a Poisson distribution with parameter λ. Derive a (1 - α)100% large sample con?dence interval for λ.
(b) To date nodes in a phylogenetic tree, the mean path length (MPL) is used in estimating the relative age of a node. The following data represent the MPL for 39 nodes (source: Tom Britton, Bengt Oxelman, Annika Vinnersten, and Kåre Bremer, "Phylogenetic dating with con?dence intervals using mean path-lengths"). Assume that the data (given in centimeters) follow a Poisson distribution with parameter λ.
65.2
47.0
38.2
13.5
18.0
25.6
16.3
14.0
23.2
18.8
7.5
13.3
11.0
54.9
22.0
50.1
32.6
26.0
13.0
9.0
7.2
4.7
4.5
41.1
45.8
37.0
8.5
30.5
29.3
13.8
7.7
5.5
24.1
12.5
22.3
19.0
9.5
3.0
Obtain a 95% con?dence interval for λ and interpret.
the mathematics department is interested in observing the performance of their first-year undergraduate students. the
a toll bridge charges 1.00 for passenger cars and 2.50 for other vehicles. suppose that during daytime hours 60 of all
the director of the irs has been flooded with complaints from the ta payers that people must wait more than 45 minutes
A random sample of students is selected, and each one is asked to try first brand A and then brand B, or vice versa with the order determined at random.
If one of the 100 employees is randomly selected, find the probability of getting someone who carpools, someone who cycles to work, or someone who works part time.
A mean of 25 inches and a standard deviation of 5 inches. What is the probability that the area receives at least 30 inches of rain in a year?
What item/s can be deleted to improve reliability, what items should never be deleted to maintain reliability of data and how many items need to be deleted to achieve maximum reliability
A startup company began manufacturing toy dolls tailored to environmental-oriented customers. Using linear regression, find a linear model for the Cost Function if the company's yearly costs for the next five years were (2005,$8,000,000),(2006,$1..
1. you manage a loan portfolio at a local bank. one day you are approached by a jim riskind who is seeking an unsecured
The researcher expects a 12-point treatment effect and plans to use a two-tailed hypothesis test with a = 0.05.
a 40-cm-diameter 90-cm-diameter vertical cylindrical container is partially filled with 60-cm-high water. now the
a well-insulated rigid tank of volume 10 ft3 contains carbon dioxide initially at 30 psia and 60 degrees f. the tank is
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