If telephone purchase orders are Poisson distributed with an average of 3 orders per minute, answer the following:

1. probability at most 3 in a 30 second interval

2. probability of at least 4 in a 45 second interval

3. probability of 1, 2, or 3, in a 60 second interval

4. probability that of 5 different 45 second intervals 2 or more of the intervals would entail at least 4 orders each

5. standard deviation of the expected number of failures in a 60 second interval

A fair 4-sided die is rolled, let X denote the outcome. After that, if X = x, then x fair coins are tossed, let Y denote the number of Tails observed. a) Find P( X >= 3 | Y = 0 ). b) Find E( X | Y = 2 ). “Hint”: Construct the joint probability distribution for ( X, Y ) first. Write it in the form of a rectangular array with x = 1, 2, 3, 4 and y = 0, 1, 2, 3, 4.

Pick one of the best answers below - thank you

The lineage leading to Homo sapiens diverged from the lineage leading to Pan troglodytes ________________ of years ago.

1. hundreds of millions

2. billions

3. thousands

4. millions

What is the difference between microevolution and macroevolution?

1. Microevolution is proven fact, and macroevolution is just a guess (a theory).

2. Microevolutionary processes are always faster than macroevolutionary processes.

3. Microevolution describes changes in allele frequencies within populations/species; macroevolution describes processes occurring above the species level.

4. Microevolution is about small changes, and macroevolution is about big changes.

What is the proper relationship between the terms “fact” and “theory”, as they are used in science?

1. Theories are guesses, but if they turn out to be correct, they become facts.

2. A hypothesis, after passing many tests against facts, becomes a theory.

3. Many facts, when added together, become a theory.

4. Theories provide systematic explanations of diverse classes of facts.

Assuming the model of Hardy-Weinberg Equilibrium, if the allele frequency of A is .6 and the allele frequency of a is .4, what are the expected genotype frequencies?

1. AA=.36, Aa=.48, aa=.16

2. AA=.60, Aa=.00, aa=.40

3. AA=.25, Aa=.50, aa=.25

4. AA=.16, Aa=.48, aa=.36

Which of the following is INCORRECT about the Urbilataria?

1. Urbilateria were probably small, bilaterally symmetrical wormlike creatures.

2. Urbilateria were the common ancestors of the three bilaterian clades.

3. Urbilateria were common in the Burgess Shale.

4. Urbilateria lived at least 560 million years ago in the Precambrian.

What are Ediacaran animals?

1. a group that includes the Cambrian Burgess Shale animals

2. a group of mainly soft-bodied animals that lived at the end of the Precambrian

3. Australian monotreme mammals

4. the group that includes starfish, sea urchins and sea cucumbers.

Phylogenetic analyses suggest that most Cambrian animals represent:

1. stem or crown groups of animal phyla.

2. Urbilateria.

3. extinct groups unrelated to living animals.

4. Precambrian relicts.

Which of the following is NOT one of the criteria for adaptive radiation?
Group of answer choices

1. monophyly

2. rapid speciation

3. contains at least hundreds of species

4. trait utility

Hagfishes and lampreys are the only living:

1. ostracoderms.

2. agnathans.

3. gnathostomes.

4. cephalochordates.

Sampling Distributions

This exercise is to be completed in a group.

For the population: 1 3 5 7 9

Find the mean and standard deviation.

Mean Calculation:

1 + 3 + 5 + 7 + 9 = 25

25 / 5 = 5

The mean is 5

Standard Deviation Calculation:

( 1 - 5 ) ² = ( -4 ) ² = 16

( 3 - 5 ) ² = ( -2 ) ² = 4

( 5 - 5 ) ² = ( 0 ) ² = 0

( 7 - 5 ) ² = ( 2 ) ² = 4

( 9 - 5 ) ² = ( 4 ) ² = 16

16 + 4 + 0 + 4 + 16 = 40

( 1 / 5 ) × 40 = 8

√( 8 ) = 2.8284

The standard deviation is ≈ 2.83

Now determine how many samples of size 2 can be formed from this population of size 5, disregarding order. Use the appropriate formula.

List all the samples of size 2 that can be formed from this population. Be sure the list is consistent with the answer obtained from the formula. Otherwise, check your work.

Calculate the mean of each of the samples of size 2.

Create a probability distribution of all the sample means from the sample of size 2. (HINT: If you have a mean of 7 in the list of sample means and it occurs 3 times out of 10, then the probability is 0.3 for that mean value.)

Calculate the mean and standard deviation of that probability distribution using the appropriate formulas.

1. Consider an arithmetic expression of the form a#b=c. Check whether it is possible to replace with one of the four signs: +, -, * or / to obtain a correct expression.

Make a MATLAB program

Consider the following time series.

(b)Use the following dummy variables to develop an estimated regression equation to account for seasonal effects in the data:

x₁ = 1 if quarter 1, 0 otherwise; x₂ = 1 if quarter 2, 0 otherwise; x₃ = 1 if quarter 3, 0 otherwise.

=

(c)Compute the quarterly forecasts for next year.

quarter 1 forecast___

quarter 2 forecast___

quarter 3 forecast___

quarter 4 forecast___

A statistical program is recommended.

Consider the following time series.

Use the following dummy variables to develop an estimated regression equation to account for seasonal effects in the data:

x₁ = 1 if quarter 1, 0 otherwise; x₂ = 1 if quarter 2, 0 otherwise; x₃ = 1 if quarter 3, 0 otherwise.

=

(c) Compute the quarterly forecasts for next year.

quarter 1 forecast

quarter 2 forecast

quarter 3 forecast

quarter 4 forecast