This post presents exercises on the lognormal distribution. These exercises are to reinforce the basic properties discussed in this companion blog post.
Let be a normal random variable with mean 6.5 and standard deviation 0.8. Consider the random variable . what is the probability ?
Suppose follows a lognormal distribution with parameters and . Let . Determine the following:
- The probability that exceed 1.
- The 40th percentile of .
- The 80th percentile of .
Let follows a lognormal distribution with parameters and . Compute the mean, second moment, variance, third moment and the fourth moment.
Let be the same lognormal distribution as in Exercise 2. Use the results in Exercise 2 to compute the coefficient of variation, coefficient of skewness and the kurtosis.
Given the following facts about a lognormal distribution:
- The lower quartile (i.e. 25% percentile) is 1000.
- The upper quartile (i.e. 75% percentile) is 4000.
Determine the mean and variance of the given lognormal distribution.
Suppose that a random variable follows a lognormal distribution with mean 149.157 and variance 223.5945. Determine the probability .
Suppose that a random variable follows a lognormal distribution with mean 1200 and median 1000. Determine the probability .
Customers of a very popular restaurant usually have to wait in line for a table. Suppose that the wait time (in minutes) for a table follows a lognormal distribution with parameters and . Concerned about long wait time, the restaurant owner improves the wait time by expanding the facility and hiring more staff. As a result, the wait time for a table is cut by half. After the restaurant expansion,
- what is the probability distribution of the wait time for a table?
- what is the probability that a customer will have to wait more than 20 minutes for a table?
- longnormal with and where is the natural logarithm.