A discrete random variable U has a probability mass function

A discrete random variable U has a probability mass function as shown below. Compute p_U (2) and E[U]. For the random variable U defined above, plot its CDF. A continuous random variable X is uniformly distributed in the interval [0, 1]. Compute its CDF. If X is defined above, a second continuous random variable Y is defined as Y = tan(3 pi/4(X - 0.5)). Compute its CDF. Compute the PDF of Y. Use the rand() function to generate N = 100000 values of the random variable X defined above. Use the histogram method to numerically compute and plot the PDF of X. Use M = 50 histogram bins. Plot the theoretical PDF of X. For the generated X values, compute the corresponding Y values. Use the histogram method to numerically compute and plot the PDF of Y. Plot the theoretical PDF of Y which you computed in 4.5. Numerically compute and display the expected values of X and Y.

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