Step by Step Solutions

(Solution Library) Suppose that X and Y follow a bivariate (standard) normal distribution with parameter -1 f_X, Y(x, y)=(1)/(2 π √1-\rho^2) \exp -1/2

Question: Suppose that $X$ and $Y$ follow a bivariate (standard) normal distribution with parameter $-1<\rho<1$, and with joint probability density function

\[f_{X, Y}(x, y)=\frac{1}{2 \pi \sqrt{1-\rho^{2}}} \exp \left\{-\frac{1}{2} \frac{\left(x^{2}-2 \rho x y+y^{2}\right)}{1-\rho^{2}}\right\}, \quad-\infty Show that the joint mgf of $X$ and $Y$ is given by

\[M_{X, Y}(s, t)=\exp \left\{\frac{1}{2}\left(t^{2}+2 \rho s t+s^{2}\right)\right\}\]

and then find the marginal mgfs of $X$ and $Y$. Using the joint and marginal mgfs, calculate the correlation between $X$ and $Y$. Show that $X$ and $Y$ are independent only when $\rho=0$.

Price: $2.99

Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document

∴ Other downloads you may be interested in ∴

Solution: Suppose that X_1 and X_2 are independent and identically

[See Solution] Suppose X_1 and X_2 have a uniform distribution

[Steps Shown] Let X and Y be independent exponential random variables

[See Solution] Suppose that two random variables X and Y have

[Solved] Suppose a researcher wanted to study the role of religious

Linear Equation Point Slope Form Calculator - MathCracker.com

(Solution Library) Suppose that X and Y follow a bivariate (standard) normal distribution with parameter -1 f_X, Y(x, y)=(1)/(2 π √1-\rho^2) \exp -1/2

reset password

sign up