Question

The c.d.f of the lifetime pH of water samples from a specific lake is a random variable X with probability density function:

F(x) = (1 − (16 /x^2)) if x ≥ 4 and 0 elsewhere

1. Find the p.d.f of X.

2. Find P(7 ≤ X ≤ 10).

Answer 1

The CDF of X is given by:

The PDF is given by:





Hence, the PDF is given by:


Here, we are to find,

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