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Assume there is an Ideal Random Number Generator which generates any real number between 0 and given integer. Two numbers are generated from the above generator using integer A and B, let's assume the numbers generated are X1 and X2. There is another integer C. What is the probability that summation of X1 and X2 is less than C.

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  • $\begingroup$ The density has the shape of a roof, starting at 0, with positive slope s on some interval (0,c), with null slope on (c,d), and with negative slope -s on (d,d+c), for some suitable s, c and d. Now, what did you try? $\endgroup$ – Did Nov 9 '13 at 11:05
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Hint:

Draw the sample space on axes $X_1, X_2$. You should get a rectangle of area $AB$. Now shade the portion $X_1 + X_2 < C$ in this rectangle.

Now consider cases where $C \in \,$ one of the following intervals $(0 < \min(A, B)), [\min(A, B), \max(A, B)], (\max(A, B), A+B), (A+B, \infty)$...

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  • $\begingroup$ can you elaborate your answer further? $\endgroup$ – Kaushal28 Jul 16 '16 at 8:03
  • $\begingroup$ @Kaushal28 Have you tried drawing for any particular case? Where do you need more elaboration? $\endgroup$ – Macavity Jul 16 '16 at 8:06
  • $\begingroup$ But I can't understand how to draw sample space on axes X1, X2. $\endgroup$ – Kaushal28 Jul 16 '16 at 8:08
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    $\begingroup$ @Kaushal28 Missed your Q. Check sketchtoy.com/67283206 The rectangle is your sample space, the shaded region is the event you're interested in. Their ratio is the probability you seek. Depending on $C$, the shaded region changes... $\endgroup$ – Macavity Jul 22 '16 at 10:28

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