Methods2024 NHT Exam 2 Section A · Q10CAS active1 mark

Value of k for a trapezium-shaped probability density function

The graph for $y = f(x)$ is shown below.

Graph of y = f(x): zero along the x-axis outside (-2, 0) and (2, 0), rising in a straight line from (-2, 0) to (-k, k), horizontal from (-k, k) to (k, k), then falling in a straight line to (2, 0), forming a trapezium above the x-axis.

Find the value of $k$ given that $f(x)$ is a probability density function.

1 mark

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