Answer: Let X and Y have a bivariate normal distribution

QUESTION:

Let \(X\) and \(Y\) have a bivariate normal distribution with parameters \(\mu_{X}=10, \sigma_{X}^{2}=9, \mu_{Y}=15, \sigma_{Y}^{2}=16\), and \(\rho=0\). Find

(a) \(P(13.6<Y<17.2)\).

(b) \(E(Y \mid x)\).

(c) \(\operatorname{Var}(Y \mid x)\).

(d) \(P(13.6<Y<17.2 \mid X=9.1)\).

Equation Transcription:

Text Transcription:

X  

Y  

mu_X=10, sigma_X^2=9,mu_Y=15,sigma_Y^2=16

rho =0  

P(13.6<Y<17.2)  

E(Y∣x)  

Var⁡(Y∣x)  

P(13.6<Y<17.2∣X=9.1)