School

University of Phoenix **We aren't endorsed by this school

Course

DAT 565

Subject

Statistics

Date

Aug 11, 2023

Pages

2

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A discrete random variable takes on a countable number of values meaning specific values with no
values in between. A discrete random variable can only take on specific values like 0, 1, 2, etc. It can't
take on values in between, like 0.5 or 1.2. Vs. A continuous random variable can take on infinite values,
which can be any real number within a certain range. A continuous random variable can take on any
value within a certain range, between 0 and 10. It can take on values like 0.5 or 1.2 or any other value.
So, the key difference between discrete and continuous random variables is that discrete variables can
only take on specific values with no values in between, while continuous variables can take on any value
within a certain range, including values in between.
A discrete random variable takes on a countable number of values, i.e., specific values with no
intermediate values. A discrete random variable can only take on specific values like 0, 1, 2, etc. Vs. A
continuous random variable can take on infinite values, which can be any real number within a certain
range. A continuous random variable can have any value between 0 and 10. So, the key difference
between discrete and continuous random variables is that discrete variables can only take on specific
values with no values in between, while continuous variables can take on any value within a certain
range, including values in between.
I work for a licensing board, so I would use the continuous random variable to ensure that licensed
professionals meet certain standards. This would be done by randomly selecting a sample of licensed
professionals and reviewing their work to ensure they meet these standards. The board could then use a
simple random selection to create new or additional procedures. Additionally, this sampling will help
them draw more accurate conclusions about the overall compatibility of the population. The use of
random sampling can help reduce bias in the selection process and increase the transparency and
integrity of the audit process.
To calculate the mean and variance of a continuous random variable, you would need to use the
probability density function (PDF) of the distribution that the variable follows. To calculate the mean,
multiply each variable value by its probability density function and then sum up all the results. This gives
you the expected value of the variable or the mean. To calculate the variance, you first subtract the
mean from each variable value, square the differences, and multiply by their probability density
function. Then, you sum up all the results. This gives you the expected value of the squared deviations
from the mean or the variance.
When we have data that follows a continuous probability distribution, we use a probability density
function (PDF) to describe the likelihood of each possible value of the variable. This PDF gives us an idea
of how likely each value is to occur.
To find the mean, multiply every possible variable value by its PDF and then add all these products. This
provides the expected value of the variable or the average value that can be expected over the long

term. The first thing needed is to find the mean to find the variance; then, for each possible value of the
variable, we subtract the mean from that value, square the difference, and multiply by the PDF.
This is done for all possible values, and then add up all of these values. This gives us the expected value
of the squared deviations from the mean. We call this the variance, and it tells us how spread out the
data is around the mean.
So, in summary, we use the probability density function to find the mean and variance of a continuous
random variable. For the mean, we multiply each possible value by its PDF and add up the products. For
the variance, we subtract the mean from each possible value, square the differences, and multiply by the
PDF. Then, we add up all of these values.

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