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. 

Given discrete joint PDF: Compute Leave your answer to 3 decimal places.

Both discrete and continuous random variables have probability functions that represent the probabilities of certain events associated with the random variable.

The time until a screen is cracked on a smart phone has a random distribution with mean μ = 500 hours of use. Denote this time by X and the process can be modelled by a Poisson process.  What distribution does X follow ?

List Kohlberg’s stages of Moral Development at the Preconventional Level

What does Kohlberg’s Theory of Moral Reasoning emphasize about actions/choices?