Question

Q 1 . ( 8 marks) Answer the following:

a) Describe the difference between a discrete and a continuous ra ndom variable. Give an example of each.

b) Under what conditions might you choose to use a dot plot rather than a histogram?

c) Differentiate between retrospective and observational studies

d) What is the significance of the Bayes’ Theorem?   

  

Answer 1

a)

Discrete random variable: random variablesthat can assume a countable number of values are calleddiscrete.

For example: the number of voters ina sample of 1000 who favor impeachment of the president: x= 0, 1, 2,........,1000

Continuous random Variable: random variables that canassume values corresponding to any of the points contained in aninterval are called continuous.

For example: the depth (in feet) atwhich a successful oil-drilling venture first strikes oil:, where c is the maximum depthobtainable.

Note that several of the examples of discrete random variablesbegin with the words The numberof......... This wording is very common, since thediscrete random variables most frequently abserved arecounts.

b)

Dot plot is a type of histogram. These are usually used when you have small finite bins and small number of objects to put into the bins.

Its relatively easy to draw and each dot represents one count. As you can see, for higher number of objects, you really can’t keep putting dots. So we employ a better of representation using bar graphs which just gives a number for the count of each bin and a relative height.

c)  

A retrospective study uses existing data that have been recorded for reasons other than research. A retrospective case series is the description of a group of cases with a new or unusual disease or treatment. ... Retrospective study designs are generally considered inferior to prospective study designs.

In an observational uncontrolled study, researchers simply watch what happens to a series of people in one group. For example, everyone gets drug X, and the researchers record how many people get better. But there's a big problem with these studies: you can't know what would have happened without drug X - maybe more people would have gotten better!

d)

he theorem provides a way to revise existing predictions or theories given new or additional evidence. In finance, Bayes' theorem can be used to rate the risk of lending money to potential borrowers.

The formula is as follows:

Bayes' theorem gives the probability of an event based on information that is or may be related to that event.