Question: answer all questions with explanation 4. Consider the mixed random variable X with a pdf fx (x) = cY + 0.256(x- 5) + 0.256(x +

answer all questions with explanation

4. Consider the mixed random variable X with a pdf fx (x) = cY + 0.256(x- 5) + 0.256(x + 5) where Y is a Gaussian random variable with a mean value of 0 and a variance of 1/4. For this problem, (a) Find the value of the constant c; (b) Sketch the pdf and cdf of X; (c) Determine P[X 4] ; (g) P[X = 5]; (h) P[X = 0]

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