Step by step of each calculation, integrals as derivative too . Let X be a random variable with CDF ?? (?) = { 1 ? ≥ 1 1/ 2 + ?/2 0 ≤ ? < 1 0 ? < 0] What kind of random variable is X: discrete, continuous, or mixed?. a. Find the PDF of ? b. Find ?(?). c. Find ?(? = 0 |? ≤ 0.5)
(a)
It is continuous distribution.
The pdf of X is
(b)
(C)
Now,
The required probability is
Step by step of each calculation, integrals as derivative too . Let X be a random...
5. (Discrete and ontinuous random variables) (a) Consider a CDF of a random variable X, 10 x < 0; Fx(x) = { 0.5 0<x< 1; (1 x > 1. Is X a discrete random variable or continuous random variable? (b) Consider a CDF of a random variable Y, 1 < 0; Fy(y) = { ax + b 0 < x < 1; 11 x >1, for some constant a and b. If Y is a continuous random variable, then what...
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