The _____________  is an example of a type of genetic drift in which rare alleles occur at a higher frequency in a population isolated from the general population.

Which of the following observations is not part of natural selection as posed by Darwin?

Explain the paradigm Uniformitarianism which was made famous by Charles Lyell. 

Explain Lamarck’s idea of acquired characteristics and how it differed from Darwin’s natural selection.  Lamarck used the idea of long neck Giraffe’s and short neck Giraffe’s, for example. Explain his idea in a sentence or two. 

At Thanksgiving, your friend laments about having to eat Brussels sprouts. Based on your knowledge of biology, you know that humans caused the evolution of Brussels sprouts through the mechanism of _____________________ selection.

Suppose the population of IQ values is normally distributed with a mean of 100 and standard deviation 15. Now we randomly sample 36 people and measure their IQs. The sum of all these data points is denoted by

It was found that, in 19th-century Prussia, an average of 0.61 soldiers died from horse kicks each year in each Prussian Army Corps. Assuming that the number of horse-kick deaths per year follows a Poisson distribution, calculate the probability that exactly two soldiers died from horse kicks in the VII Army Corps in 1898.

Suppose population of IQ values is normally distributed. The mean is 100 and standard deviation is 15. Now we randomly pick a person and measure their IQ, denoted by X.  Evaluate . 

Suppose we are interested in finding the probability of obtaining at least a 5 or 6 in four rolls of a fair die (each face will have same chance to appear). If the r.v. X denote the number of times a 5 or 6 appears in the four rolls, what distribution does X follow ?

If the joint PDF (or PMF) of is such that for every in the sample space,  the random variables X and Y are independent. Here, and denote the marginal PDF (or PMF) of X and Y respectively.