Question

Let X be a random variable with a cumulative distribution function.
F(x) = `{{:(0",",  "if"  x  < 0),(x/8",",  "if"  0 ≤ x ≤ 1),(1/4 + x/8",",  "if"  1 ≤ x ≤ 2),(3/4 + x/12",",  "if"  2 ≤ x < 3),(1",",  "for"  3 ≤ x):}`
Is X a discrete random variable? Justify your answer

Answer 1

W.K.T Probability density Function

f(x) = `("d"["F"(x)])/("d"x)`

f(x) = `{{:(1/8,  "if"  0 ≤ x < 1),(1/8, "if" ≤ x < 2),(1/12,  "if"  2 ≤ x  3),(0,  "elsewhere"):}`

 X is not discrete since f is not a step function.