IS4303 IT-Mediated Financial Solutions and Platforms

Assessment Brief:

• Course Code: EDST2000
• Course Title: IT-Mediated Financial Solutions and Platforms
• University: Singapore University of Social Sciences
• Words: 1000+
• Country: SG
• Referencing Styles: As Per Required

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Problem 1. Let X be a constant random variable and FX(x) be its cumulative distribution function (CDF). Question-i (5 pts): Let X be a random variable following the Rayleigh distribution with parameter σ = 1. Generate N = 100000 realizations of FX(X) (i.e., plug X into its own CDF. Note that FX(X) is a random variable). Plot the empirical CDF and plot the empirical pdf (histogram). What is the distribution of FX(X)? The cumulative frequency function of a Rayleigh random variable is given in the HW4 equation

(1). Please set σ = 1. You can use the built-in function in MATLAB (e.g., Method 2 in HW4) to generate realizations of the Rayleigh random variable. Question-ii (5 pts): If X is a standard normal random variable (set µ = 0 and σ = 1), plot the empirical CDF and empirical pdf (histogram) of FX(X) with N = 100000. What is the distribution of FX (X)