In Chapter 6, we continue to discuss about probability with a focus on continuou
ID: 3257876 • Letter: I
Question
In Chapter 6, we continue to discuss about probability with a focus on continuous probability distributions. In a continuous probability distribution, the variable can have an value within a range.
In this class, I could ask all of you to report the distance from your home to the closest movie theatre in miles. Everyone of you could respond with a different value: .4 miles, 1.2 miles, 2.65 miles, etc...
The most common continuous distribution is the standard normal distribution. For this week, select a continuous random variable (be sure to describe it), and explain whether you think it is best characterized as a uniform or normal distribution.
Explanation / Answer
Let us consider a variable : Blood pressure of a person. Note that, the blood pressure of a person can range any positive values. So, by definition, it is a continuous variable. Typically, a normal curve is bell shaped frequency curve and it has a peak at its mean which is same as median, And most importantly, most of the values of the normal distribution tend to concentrate/cluster around the mean/median, which otherway tells that it is a light tailed distribution. Now, for the variable blood pressure, we expect that, most of the people have BP around 120 and the proportion of human with BP much higher and much lower than 120 is very less, i.e. most of the people's BP will cluster around the peaked value. So, Blood pressure is an example of Normal distribution.
Consider the Cumulative distribution function of a normal distribution. From the property of CDF, it can take any values between 0 and 1. So, the CDF of normal dstribution is a uniform distribution.