is a probability density function for a particular random variable $$f ( x ) = \left\{ \begin{array} { l r }
\frac { 1 } { 3 } & \text { for } 0 \leq x \leq 3 \
0 & \text { otherwise }
\end{array} \right.$$ variable X . Use integration to find $P ( 0 \leq x \leq 1 )$ rounded to the nearest hundredth.
A) 0.67
B) 0.22
C) 0.12
D) 0.33

Question

is a probability density function for a particular random variable $$f ( x ) = \left\{ \begin{array} { l r } 
\frac { 1 } { 3 } & \text { for } 0 \leq x \leq 3 \
0 & \text { otherwise }
\end{array} \right.$$ variable X . Use integration to find $P ( 0 \leq x \leq 1 )$ rounded to the nearest hundredth.
A) 0.67
B) 0.22
C) 0.12
D) 0.33

Quizplus · Accepted Answer

To find $P(0 \leq x \leq 1)$, integrate the probability density function $f(x) = \frac{1}{3}$ from 0 to 1. The integral is $\int_{0}^{1} \frac{1}{3} dx = \frac{1}{3}x \big|_{0}^{1} = \frac{1}{3}(1 - 0) = \frac{1}{3}$, which rounds to 0.33.

Is a Probability Density Function for a Particular Random Variable f(x)={13 for 0≤x≤30 otherwise f ( x ) = \left\{ \begin{array} { l r } \frac { 1 } { 3 } & \text { for } 0 \leq x \leq 3 \\0 & \text { otherwise }\end{array} \right.f(x)={31​0​ for 0≤x≤3 otherwise ​

Is a Probability Density Function for a Particular Random Variable $f ( x ) = \left\{ \begin{array} { l r } \frac { 1 } { 3 } & \text { for } 0 \leq x \leq 3 \\0 & \text { otherwise }\end{array} \right.$