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Solve the following in R Let X be a random variable that is normally distributed with mean 10 and standard deviation 2. Let Y be

Solve the following in R

Let X be a random variable that is normally distributed with mean 10 and standard deviation 2.

Let Y be a random variable that is normally distributed with mean 15 and standard deviation 1.

Let Z be a random variable that is 2X +3Y.

  1. Use simulation to estimate the correlation of Y and Z. What is your estimate of the correlation?
  2. Using your estimate from the previous part, and without additional simulation, what is the variance of Y + Z?
  3. Simulate Y + Z. What is the estimated variance of Y + Z based on the simulation?

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