Question

(Temperature Model) The meteorologist models today's and tomorrow's temperatures T0 and T1
relationship between the two
T1 = T0 + ∆T
where ∆T describes the temperature change. Random variables T0 and ∆T are assumed to be different
independent. It is also known that E (T0) = µ and Var (T0) = σ²
and E (∆T) = 0 and
Var (∆T) = θ²
. Model parameters µ, σ> 0 and θ> 0 are assumed to be known in advance.
(a) Specify E (T1).
(b) Specify SD (T1).
(c) Specify Cov (T1, T0).
(d) Determine Cor (T1, T0). Before calculating the exact value of the correlation, try intuitively
to conclude, through the interpretation of correlation, how it behaves in cases θ → 0 and θ → ∞.

Answer 1

Temperature Model is provided to us and we find the mean and variances of random variables T1 and T0