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Find k such that the function f defined byfX (x) =kx2, 0 < x < 1,0, otherwiseis a probability density function. Also, determine P (1/3 < X ≤ 1/2

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Find k such that the function f defined byfX (x) =kx2, 0 < x < 1,0, otherwiseis a probability density function. Also, determine P (1/3 < X ≤ 1/2
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Solution 1

To find the value of k such that the function f is a probability density function, we need to ensure that the integral of f from -∞ to ∞ is equal to 1, because the total probability must be 1.

The function f is only non-zero between 0 and 1, so we only need to integrate from 0 to 1:

∫ from 0 to 1 Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.

Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
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