Question

S5.6 Let $X$ be a random variable with cumulative distribution function \begin{equation} F_X(x) = \begin{cases} 0 & \text{if } x < 0\\ x & \text{if } 0 \le x \le 1\\ 1 & \text{if } x > 1 \end{cases} \end{equation} Then $P(3X \le 1)$ equals (A) 1/6 (B) 1/4 (C) 1/3 (D) 1/2 (E) none of the above.

          S5.6 Let $X$ be a random variable with cumulative distribution function
\begin{equation*}
F_X(x) = \begin{cases} 0 & \text{if } x < 0\\ x & \text{if } 0 \le x \le 1\\ 1 & \text{if } x > 1 \end{cases}
\end{equation*}
Then $P(3X \le 1)$ equals
(A) 1/6
(B) 1/4
(C) 1/3
(D) 1/2
(E) none of the above.

S5.6 Let X be a random variable with cumulative distribution function

FX(x) = 0 if x < 0
x if 0 ≤ x ≤ 1
1 if x > 1

Then P(3X ≤ 1) equals
(A) 1/6
(B) 1/4
(C) 1/3
(D) 1/2
(E) none of the above.

Added by Andrew L.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Ahmet Yavas

05/29/2022

Step 1

Step 1: We need to find the probability that 3X is less than or equal to 1. Show more…

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S5.6 Let X be a random variable with cumulative distribution function $$F_X(x) = \begin{cases} 0 & \text{if } x < 0 \\ x & \text{if } 0 \le x \le 1 \\ 1 & \text{if } x > 1 \end{cases}$$ Then P(3X ≤ 1) equals (A) 1/6 (B) 1/4 (C) 1/3 (D) 1/2 (E) none of the above.