Learning Journal Unit 5 Statistics

We are now covering material that is not common knowledge, and it is now very important to include citations when you use an idea from another source (book, Internet, etc). Be sure to add a citation and reference entry for the definition questions below.

1. What is an exponential distribution (include an APA citation)? ____

In probability theory and statistics, the exponential distribution (also known as negative exponential distribution) is the probability distribution that describes the time between events in a Poisson point process, i.e. a process in which events occur continuously and independently at a constant average rate (en.wikipedia.org).

1. When would you use an exponential distribution? _____________

The exponential distribution is often concerned with the amount of time until some specific event occurs. For example, the amount of time from now until an earthquake occurs has an exponential distribution(en.wikipedia.org).

1. What is a binomial distribution (include an APA citation)?________

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments (en.wikipedia.org).

1. When would you use a binomial distribution? _________________

The binomial distribution model allows us to compute the probability of observing a specified number of "successes" when the process is repeated a specific number of times i.e. in a set of patients and the outcome for a given patient is either a success or a failure.

3. Task

Run these commands in R, then use your own words to describe what the resulting numbers represent. You can get some information about the functions by using the help commands in R (such as ?pbinom to get information about the pbinom() command in R):

1. pbinom(q=5, size=10, prob=1/6)

[1] 0.9975618

The function pbinom () returns the cumulative probability function for binomial distribution with parameters size n (10 in this case), with the probability of success = 1/6.

Prefix p provides the probability (based on area under the distribution curve) of a given observation falling below a specified value, deduced based on the area under the distribution curve to the left of the specified value.

b)

n=10
p=.5
x=9
pbinom(x, n, p)

[1] 0.9990234

This function is the same as the previous function (for determining cumulative probability distribution value for Binomial distribution) except that in this case the values of x, n and p are separately assigned.

1. c) punif(5, min=1, max=10) - punif(4, min=1, max=10)

[1] 0.1111111

The function punif() provides cumulative density function for a uniform distribution (it gives the area to the left of value 5 for a given uniform distribution with minimum value of 1 and maximum 10)

If we separately run these commands then firstly the area to the left of x=5 is computed and then area to the left of x=4 is computed.

Then the difference between the area of these two values (x=5 and x=4) will provide the area between these two numbers.

References,

Yakir, B. (2011). Introduction to Statistical Thinking (With R, Without Calculus). Jerusalem, IL: The Hebrew University of Jerusalem, Department of Statistics.

Exponential distribution. Retrieved from. https://en.wikipedia.org/wiki/Exponential_distribution