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lyudmila [28]
2 years ago
14

A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after th

e hour. Let X = the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is as follows. f(x) = kx2 0 ≤ x ≤ 2 0 otherwise (a) Find the value of k. (Enter your answer to three decimal places.)
Mathematics
1 answer:
Citrus2011 [14]2 years ago
4 0

Answer:

Value of k is \displaystyle\frac{3}{8}      

Step-by-step explanation:

We are given the following information in the question:

f(x) = kx^2, 0\leq x \leq 2\\~~~~~~~= 0, \text{ otherwise}

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,

\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}

Hence, value of k is \displaystyle\frac{3}{8}

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