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Signal and systems miscellaneous

Signals and Systems

  1. Mean of X if
    fx(x) =
    3(1 – x)2; for 0 ≤ x ≤ 1
    0; otherwise
    1. 1
      3
    2. 1
      2
    3. 1
      4
    4. 1
      5
Correct Option: C

μx = E[X] = xfx(x)dx
– ∞

= 1x.3(1 – x) 2dx
0

= 31(x – 2x2 + x3)dx
0

= 3
x2
-
2x3
+
x4
1
2340

= 3
1
-
2
+
1
234

= 3
6 - 8 + 3
=
1
124



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