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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.
Use the permutations rule to determine the total number of different ways the winners can be drawn.
The State of Ohio plays a daily (except Sunday) three digit lottery, where the player chooses any three numbers, 1 thru 10, three different times.
The number of lightning strikes in a year at the top of a particular mountain has a Poisson distribution with a mean of 4.2. Find the probability that in a randomly selected year, the number of lightning strikes is 0.
assume john is conducting a one-way anova with three groups. naturally he specifies the null hypothesis as
For a population with a mean of μ = 50 and a standard deviation of σ = 10, how much error, on average, would you expect between the sample mean (M) and population mean for:
Q6: A global financial institution transfers a large data file every evening from offices around the world to its headquarters. The time required to process the file is normally distributed with mean of 1.5 hours and standard deviation of 15 minutes.
Determine the percent of the days is the price between $38.00 and $40.00?
a random sample of 900 individuals has been selected from a large population. it was found that 180 are regular users
A researcher claims the average American drinks 52 gallons of cola per year with a population standard deviation of 2.0 gallons. We sample 25 random people and find the mean yearly consumption was 49 gallons.
You are playing poker and you are dealt the A, K, Q, J, 10 of spades.
For the data giben below, prepare a R-chart. Note that the sample size is three.
write a 1050- to 1400-word paper in which you complete the following1 explain the organizational and societal functions
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