Question

Problem 4.4 (20 points): Continuous RV The cumulative distribution function of random variable X is \begin{cases} 0, & x < -1 \\ \frac{(x+1)}{2}, & -1 \le x < 1 \\ 1, & x \ge 1 \end{cases} a) What is the probability $P[X > 1/2]$? b) What is the probability that $P[-1/2 \le X < 3/4]$? c) What is the probability that $P[|X| < 1/2]$?

          Problem 4.4 (20 points): Continuous RV
The cumulative distribution function of random variable X is
\begin{cases}
0, & x < -1 \\
\frac{(x+1)}{2}, & -1 \le x < 1 \\
1, & x \ge 1
\end{cases}
a) What is the probability $P[X > 1/2]$?
b) What is the probability that $P[-1/2 \le X < 3/4]$?
c) What is the probability that $P[|X| < 1/2]$?

Problem 4.4 (20 points): Continuous RV
The cumulative distribution function of random variable X is

0, x < -1

((x+1))/(2), -1 ≤x < 1

1, x ≥1

a) What is the probability P[X > 1/2]?
b) What is the probability that P[-1/2 ≤ X < 3/4]?
c) What is the probability that P[|X| < 1/2]?

Added by April M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Pritesh Ranjan

11/06/2023

Step 1

Step 1: We know that for a continuous random variable X, the probability of X being greater than a value a is given by: $$P(X>a) = 1 - F_x(a)$$ Show more…

Show all steps

Thanks for your feedback!

Problem 4.4 (20 points): Continuous RV The cumulative distribution function of random variable X is $$F_x(x) = \begin{cases} 0, & x<-1 \\ \frac{(x+1)}{2}, & -1\leq x<1 \\ 1, & x\geq 1 \end{cases}$$ a) What is the probability P[X > 1/2]? b) What is the probability that P[-1/2 ≤ X <3/4]? c) What is the probability that P[|X|<1/2]?