A program consists of two modules executed sequentially. Let f1(t) and…
2007
A program consists of two modules executed sequentially. Let f1(t) and f2(t)respectively denote the probability density functions of time taken to execute the two modules. The probability density function of the overall time taken to execute the program is given by
- A.
f1(t) + f2(t)
- B.
∫t0f1(x), f2(x) dx
- C.
∫t0f1(x), f2(t - x) dx
- D.
max (f1(t), f2(t))
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Correct answer: C
When two modules execute sequentially, the total time is the sum of their individual execution times. If T1 and T2 are independent random variables with PDFs f1(t) and f2(t), the PDF of their sum T = T1 + T2 is given by the convolution integral: f(t) = ∫₀ᵗ f₁(x)f₂(t−x)dx.