The probabilities of landing on 1, on 2, on 3, on 4, on 5 or on 6 when rolling a biased dice are shown in the table below.
1 answer:
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Answer
(a)
(b)
Step-by-step explanation:
(a) δ(t)
where δ(t) = unit impulse function
The Laplace transform of function f(t) is given as:
where a = ∞
=>
where d(t) = δ(t)
=>
Integrating, we have:
=>
Inputting the boundary conditions t = a = ∞, t = 0:
(b)
The Laplace transform of function f(t) is given as:
Integrating, we have:
Inputting the boundary condition, t = a = ∞, t = 0: