Consider the following function: f(z) = (x-5), 5< < 10. (a) Show that f(x) satisfies properties 1 and 2 on page 93 of a continuous probability density function. (b) Plot f(x). (c) Derive and plot f(æ)'s cumulative probability function, F(x). (d) Calculate P(X < 8), P(X > 6), and P(7 < X < 8) by hand. (e) Calculate P(X < 8), P(X 2 6), and P(7 < X < 8) using the function integrate().

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A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…