Binomial Distribution

Given mean, and variance,

and

Step 1: Recognize the Distribution
This is a binomial distribution problem, as the die is tossed 5 times with success defined as getting an odd number.
The probability of success (getting an odd number) is: Thus, the probability of failure is also .
Step 2: Use the Variance Formula for Binomial Distribution
The variance for a binomial distribution is given by: where is the number of trials (5 in this case), and is the probability of success.
Substituting the values:
Step 3: Conclusion
Thus, the variance of the distribution is .