Laplace transform of a pulse function of magnitude E and duration from t = 0 to t = a is

f(t) = e^-2t + e^-3t.

Because present output of y(n) depend upon past y(n - 1) and future y(n + 1).

Because Unit step is a Power signal. So By trignometric identifies d(t) also power.

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DC meter reads mean value.

If

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Include unity circle and exterior of circle hence x(z) will be stable, causal.

£f(t) =

£^-1F(s) = f(t)

£[a f₁(t) + bf₂(t)] = aF₁(s) + bF₂(s)

where

£[f(t - T)] = e^-sT F(s)

£[e^-at f(t)] = F(s + a)

Initial value theorem

Final value theroem

Convolution Integral

where t is dummy variable for t.

For causal output must depend upon Present and past not on future.

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The probability that first ball is white is and the probability the second ball is white is . The probability that both are white is .