C) A constant value C can be modeled as a pdf with only one non-zero entry. Recall that the pdf can only contain non-negative values and that the area under a continuous pdf (or equivalently the sum of a discrete pdf) must be 1.1) Plot the pdf of a discrete random variable X that is a constant of value C.2) Plot the pdf of a continuous random variable Y that is a constant of value C.3) Using convolution, determine the pdf of a continuous random variable Z where Z = X + Y. Here, X has a uniform distribution on [0, 3] and Y is a constant of value 2. Assume that X and Y are independent.
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