Question: Problem 4. Consider the following game. Let X be a continuous random variable which is uniform on [0,2]. You sample a value of X and

Problem 4. Consider the following game. Let X be a continuous random variable which is uniform on [0,2]. You sample a value of X and win an amount of points depending on the value you sampled. If the value of X is in [0, 1], then you win X many points. If the value of X is in (1,3/2], then you win 2X many points. If the value of X is greater than 3/2, then you win 10 points. Let W be the amount of points you win. (a) Find the cdf of W and sketch its graph. (b) Is W adiscrete random variable, a continuous random variable, or neither? Justify your

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