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Signal and systems miscellaneous
  1. Probability function when output Z(t) related to input y(t) as Y = √Z, and probability density function of input
    p(y) =
    e– y; 0 < y < ∞
    0; – ∞ < y < 0
    1. 2√z e– √z
    2. – e√z
      2√z
    3. e– z
    4. ez
Correct Option: A

Let Y = √2 z = g(y)

g′(y) =
1
z–1/2 =
1
22√z

fz(z) =
fy(y)
 =
e-y
 = 2√ze- √z
g′(y)
1
2√y


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