Statistics Solutions

[See Solution] (a) Solve the initial value problem y^prime \prime-4 y^prime+4 y=0, \text with y(0)=3 \text and y^prime(0)=1 \text . (b) Consider the function

Question: (a) Solve the initial value problem

\[y^{\prime \prime}-4 y^{\prime}+4 y=0, \quad \text { with } y(0)=3 \text { and } y^{\prime}(0)=1 \text { . }\]

(b) Consider the function

\[f(t)= \begin{cases}0, & \text { if } 02 \pi\end{cases}\]
  1. Express \(f\) in terms of the Heaviside function.
  2. State the second "t-shifting" Theorem.
  3. Use the expression you have obtained in part (i) and the shifting theorem you stated in part (ii) to find the Laplace transform of \(f(t)\). (No marks will be awarded if you calculate the Laplace transform directly.)

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