The average annual wind speed, X, at Bradfield in West Yorkshire has the following probability density function:
f(x)= \begin{cases} 2txe^{-tx^2} & x > 0, \\ 0 & \text{otherwise.} \end{cases}
For three randomly selected years, we observe the following average wind speeds:
\begin{multline} x_1 = 5.5 \\ x_2 = 3.5 \\ x_3 = 5.5 \end{multline}
a)
Find the likelihood function for t:
L(t\vert x)=\input
b)
Hence find the log-likelihood function for t:
l(t\vert x)=\input