Determine the mean and variance of the random variable in Exercise 3-16.
Answer
Step 1 of 1
(a)
We have a sample space of a random experiment which is,
Each outcome is equally likely.
A random variable is defined as follows:
outcome |
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We are asked to find the mean and variance of the random variable.
The probability mass function (PMF) of a discrete random variable is the function
The probability mass function is sometimes called the probability distribution.
Since we have given each outcome is equally likely.
Then the probability of each outcome is
Let denote the random variable.
Hence the range can take values from the table,
We can write the probability according to the definition of probability mass function (PMF),
Hence we can form the probability mass function (PMF) table:
The mean or expected value of the discrete random variable denote a
is
……….(1)
Using the PMF table, we can write the mean of a random variable,
Hence the mean of a random variable is
The variance of the discrete random variable denote a
is
……….(2)
Hence the variance of a random variable is
