Based the density function of the observed outcome, the probability
is equal to 0.1388.
<h3>What is a density function?</h3>
A density function can be defined as a type of function which is used to represent the density of a continuous random variable that lies within a specific range.
Given the following density function:
![f(x)=\left \{ {{2(1-x),\;0 < x < 1} \atop {0,\; otherwise}} \right.](https://tex.z-dn.net/?f=f%28x%29%3D%5Cleft%20%5C%7B%20%7B%7B2%281-x%29%2C%5C%3B0%20%3C%20x%20%3C%201%7D%20%5Catop%20%7B0%2C%5C%3B%20otherwise%7D%7D%20%5Cright.)
Next, we would calculate
;
![P(x\leq \frac{1}{3} )=\int\limits^\frac{1}{3} _0 {f(x)} \, dx \\\\P(x\leq \frac{1}{3} )=2 \int\limits^\frac{1}{3} _0 {(1-x)} \, dx \\\\P(x\leq \frac{1}{3} )=2|x-\frac{x^2}{2} |\limits^\frac{1}{3} _0\\\\P(x\leq \frac{1}{3} )=2[\frac{1}{3} -\frac{1}{2} (\frac{1}{3})^2]\\\\P(x\leq \frac{1}{3} )=2[\frac{1}{3} -\frac{1}{18}]\\\\P(x\leq \frac{1}{3} )=0.1388](https://tex.z-dn.net/?f=P%28x%5Cleq%20%5Cfrac%7B1%7D%7B3%7D%20%29%3D%5Cint%5Climits%5E%5Cfrac%7B1%7D%7B3%7D%20_0%20%7Bf%28x%29%7D%20%5C%2C%20dx%20%5C%5C%5C%5CP%28x%5Cleq%20%5Cfrac%7B1%7D%7B3%7D%20%29%3D2%20%5Cint%5Climits%5E%5Cfrac%7B1%7D%7B3%7D%20_0%20%7B%281-x%29%7D%20%5C%2C%20dx%20%5C%5C%5C%5CP%28x%5Cleq%20%5Cfrac%7B1%7D%7B3%7D%20%29%3D2%7Cx-%5Cfrac%7Bx%5E2%7D%7B2%7D%20%7C%5Climits%5E%5Cfrac%7B1%7D%7B3%7D%20_0%5C%5C%5C%5CP%28x%5Cleq%20%5Cfrac%7B1%7D%7B3%7D%20%29%3D2%5B%5Cfrac%7B1%7D%7B3%7D%20-%5Cfrac%7B1%7D%7B2%7D%20%28%5Cfrac%7B1%7D%7B3%7D%29%5E2%5D%5C%5C%5C%5CP%28x%5Cleq%20%5Cfrac%7B1%7D%7B3%7D%20%29%3D2%5B%5Cfrac%7B1%7D%7B3%7D%20-%5Cfrac%7B1%7D%7B18%7D%5D%5C%5C%5C%5CP%28x%5Cleq%20%5Cfrac%7B1%7D%7B3%7D%20%29%3D0.1388)
Read more on probability here: brainly.com/question/25870256
Authoritarian
Explanation: An authoritarian ruler is basically a dictator, not allowing any freedom of choice. Authoritative provides some parental control, but probably with limits. Permissive is lenient.
This is called in physics refraction phenomenon.
It occurs when light when the light passes from one medium with density d1 to another medium with density d2. The sight of the archer travel from air to deep into water & provokes a refraction.
In the excretory system, the waste materials are filtered from the blood. They are gotten rid off in order to maintain internal chemical homeostasis.
<h3>What is the Excretory System?</h3>
The excretory system can be described as a biological system that aids the body in removing unwanted materials from fluids of the body of organisms.
The main reason for the function of the excretory system is to maintain internal chemical homeostasis and prevent the body from damage.
Learn more about the excretory system on:
brainly.com/question/1171674
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Answer: Yes, I am cause you will never know what will happen when you are done falling . Sheila Josephs helps you inspires you . That's what psychologist do they talk to you the help you.