Kizspy | Question: 33
(Choose 1 answer)
(See picture)
A. (i)
B. (ii)
C. (iii)
D. (iv)
Let W = [XY]T be a 2-dimensional random variable with normal distribution W = Ν(μ,Σ), in which
\mu=[\begin{matrix}1&0\end{matrix}]^{T},\Sigma=[\begin{matrix}1&0\\ 0&2\end{matrix}].
Find the formula for the probability density function p(x,y) of W.
(i)p(x,y)=\frac{1}{2\pi\sqrt{2}}e^{-\frac{(x-1)^{2}}{2}-\frac{y^{2}}{4}}
(ii)p(x,y)=\frac{1}{2\pi\sqrt{2}}e^{-\frac{(x-1)^{2}}{4}-\frac{y^{2}}{2}}
(iii)p(x,y)=\frac{1}{2\pi\sqrt{2}}e^{-\frac{x^{2}}{4}-\frac{(y-1)^{2}}{2}}
(iv)p(x,y)=\frac{1}{2\pi\sqrt{2}}e^{-\frac{x^{2}}{2}-\frac{(y-1)^{2}}{4}}
