As an upgrade to your program, more complex calculations can be processed and the outputs of

calculations can be sent directly to a financial analysis program to aid in generating automated financial reports. There are concerns by your superiors about outputs of calculations being lost in transit from

your calculator program to the financial analysis program which could lead to errors in the

automatically-generated financial report. Explain to your superiors how the operating system will

ensure there is no loss in transmitted information from the calculator program to the financial analysis

program

2 (15) Indicate whether the following are true or false: (a) COV(X, Y) = COV(Y, X) for all random variables X and Y. (b) If two random variables are jointly Gaussian, they must be marginally Gaussian. (c) If two random variables are marginally Gaussian, they may be jointly Gaussian. (d) The pdf of X+Y always equals the convolution of the pdfs of X and Y (e) If two random variables are independent, they must be uncorrelated.5. Let X1, ..., Xn be a random sample from Uniform(0, 0) with an unknown endpoint 0 > 0. We want to estimate the parameter 0. (a) Find the method of moments estimator (MME) of 0. (b) Find the MLE 0 of 0. (c) (R) Set the sample size as 25, do a simulation in R to compare these two esti- mators in terms of their bias and variance. Include a side-by-side boxplot that compares their sampling distributions