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Two genes’ expression values follow a bivariate normal distribution. Let X and Y denote their expression...

Two genes’ expression values follow a bivariate normal distribution. Let X and Y denote their expression values respectively. Also assume that X has mean 9 and variance 3; Y has mean 10 and variance 5; and the covariance between X and Y is 2.

In a trial, 50 independent measurements of the expression values of the two genes are collected, and denoted as 11 ( , ) XY, …, 50 50 ( , ) XY. We wish to find the probability ( 0.5 ) P X Y , that is, the probability that the sample mean for the second gene exceeds the sample mean of the first gene by more than 0.5.

Conduct a Monte Carlo simulation to approximate this probability, providing a 95% confidence interval for your estimation. Submit your R script for the Monte Carlo simulation, and a brief summary of the actual simulation results.

Math   Statistics-And-Probability   
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