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2. The mean of the random variable Y is twice the mean of the random variable X, and the standard deviation of Y is twice that of X. If Y = a X + b, then determine the values of a and b. 3. For a large set of random numbers, three statistics can be used as a quick (and first) test for uniform randomness: Mean, Variance and Expectation of the autocorrelation, that is, E(ujui+1) = E(ui)E(Ui+1). Compute these values and then use that test to check the uniform Random Number Generator (RNG) in the C library. 4. Use the values of Mean, Variance and Expectation of the autocorrelation to check the quality of a uniform multiplicative RNG implemented by you on the basis on the course formula. 5. Show that the above RNG in the C library and the multiplicative RNG implemented by you do indeed pass the chi-squared test. 6. Check the quality of the random numbers generated by the above two RNG by means of a static Monte Carlo simulation (e.g. to compute the value of )