A technician wants to measure the rate at which files are transferred in a local network. She defines a continuous random variable X as the time it takes to transfer a file between two computers in seconds. The technician discovers that X has the following PDF: \(f(t) = \begin{cases} at + b & \text{if } 0 < t < 4; \\ 0 & \text{otherwise.} \end{cases}\) In expectation, it takes 3.0 seconds to transfer a file between two computers. (a) Find $a$ and $b$ which make this a valid PDF. (b) Evaluate $Pr(X - 2 \le Var(X))$.
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This means that the area under the PDF curve must equal 1, and the PDF must be non-negative for all values of t. Show more…
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