Question: Let X be a random variable with the following CDF a. Plot FX(x) and explain why X is a mixed random variable. b. Find P(X

Let X be a random variable with the following CDF Fx(x) = 0 X x + 371/172 1 for x < 0 for 0 < x < for x

a. Plot FX(x) and explain why X is a mixed random variable.

b. Find P(X ≤ 1/3).

c. Find P(X ≥ 1/4).

d. Write CDF of X in the form of FX(x) = C(x) +D(x), where C(x) is a continuous function and D(x) is in the form of a staircase function, i.e., D(x) = u( - ). k

e. Find c(x) = d/dx C(x).

f. Find EX using

Fx(x) = 0 X x + 371/172 1 for x < 0 for 0 < x < for x

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