Let X Denote the Amount of Time for Which a Book

question 3

Essay

Let X denote the amount of time for which a book on 2-hour reserve at a college-library is checked out by a randomly selected student and suppose that X $f ( x ) = \left\{ \begin{array} { l l } .5 x & 0 \leq x \leq 2 \\0 & \text { otherwise }\end{array} \right.$ Calculate the following probabilities:
a. $$P (\bar{ X} \leq 1 )$$
b. $P ( .5 \leq \bar{X} \leq 1.5 )$

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Definitions:

Amino Acids

Organic compounds that combine to form proteins, serving as the building blocks of life and playing a central role in biological processes.

Carbon-13:Carbon-12

This ratio is used in scientific studies to understand various processes such as photosynthesis and to trace the path of carbon through ecosystems due to the distinct signatures of carbon-13 and carbon-12.

Hominin Diet

The range of foods consumed by human ancestors and relatives, which varied significantly over time and with environmental conditions.

Grasses

A large and diverse family of plants, known scientifically as Poaceae, which includes wheat, corn, and rice, and is characterized by narrow leaves growing from the base.