Final answer:
The geometric mean of a set of random variables follows a lognormal distribution. In this case, simulating lognormal (5, 1) random variables and taking their geometric mean is likely to be close to ^5.5, which is approximately 244.6919.
Step-by-step explanation:
The geometric mean of a set of random variables follows a lognormal distribution. In this case, you are simulating lognormal (5, 1) random variables and taking their geometric mean. The parameters of the lognormal distribution are the mean (μ) and standard deviation (σ) on a logarithmic scale.
To calculate the geometric mean, you need to calculate the mean and standard deviation of the underlying normal distribution. The mean of the lognormal distribution () can be found using the formula = ^+1/2^2, where is the base of the natural logarithm. In this case, = ^(5+1/2(1)^2) = ^5.5.
Therefore, when you simulate a large number of lognormal (5, 1) random variables and take their geometric mean, it will likely be close to ^5.5, which is approximately 244.6919.