Simulate random numbers from log normal distribution.

X$1$~log normal $(10,3)$ with sample size,

n$=30.$

X$2$~log normal $(10,3)$ with sample size,

n$=100.$

X$3$~log normal $(10,3)$ with sample size,

n$=1000.$

i$.$For comparisons, estimate the parameter using the maximum likelihoodestimation method for each sample, X$1,$ X$2$ and X$3.$

ii$.$ Repeat this simulation for $300$ times. Each time, obtain the parameterestimates using the MLE. Compute the mean of both parameter estimates.

iii. From $($ii$),$ compute the bias and root mean square error. Discuss yourfindings.