Area Under a Linear Density Function

00:00 5 marks

Given the function \(f(x) = kx\) on the interval \(0 \le x \le 2\) and \(f(x) = 0\) elsewhere, determine the value of \(k\) such that \(f(x)\) is a probability density function. Then, find the probability that a random variable \(X\) with this density lies in the interval \([1, 2]\).

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Hint

First, use the property that the integral of a probability density over its domain equals 1.

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k = \(\tfrac{1}{2}\) and the probability for \([1,2]\) is \(\tfrac{3}{4}\)

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Area Under a Linear Density Function

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