A program consists of two modules executed sequentially. Let f1(t) and f2(t)…
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.
∫₀ᵗ f1(x)f2(x) dx
- C.
∫₀ᵗ f1(x)f2(t-x) dx
- D.
max(f1(t) + f2(t))
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Correct answer: C
The total execution time is the sum of two independent module times. The probability density of a sum of independent random variables is the convolution of their density functions: integral from 0 to t of f1(x) f2(t-x) dx.