Answer:
Value of k is [tex]\displaystyle\frac{3}{8}[/tex]
Step-by-step explanation:
We are given the following information in the question:
[tex]f(x) = kx^2, 0\leq x \leq 2\\~~~~~~~= 0, \text{ otherwise}[/tex]
where x is the time elapses between the end of the hour and the end of the lecture.
We have to find the values of k.
Since, f(x) is the pdf, then,
[tex]\displaystyle\int^\infty_{-\infty} f(x) = 1\\\\\displaystyle\int^2_{0} f(x) = 1\\\\\displaystyle\int^2_{0} kx^2 = 1\\\\k\bigg[\frac{x^3}{3}\bigg]^2_0 = 1\\\\k\times \frac{8}{3} = 1\\\\k = \frac{3}{8}[/tex]
Hence, value of k is [tex]\displaystyle\frac{3}{8}[/tex]
