For a pair of gallinules, let X equal the weight in grams

QUESTION:

For a pair of gallinules, let \(X\) equal the weight in grams of the male and \(Y\) the weight in grams of the female. Assume that \(X\) and \(Y\) have a bivariate normal distribution with \(\mu_{X}=415, \sigma_{X}^{2}=611, \mu_{Y}=347, \sigma_{Y}^{2}=689\), and \(\rho=-0.25\). Find

(a) \(P(309.2<Y<380.6)\).

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

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

(d) \(P(309.2<Y<380.6 \mid X=385.1)\).

Equation Transcription:

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Text Transcription:

X  

Y  

X=415, sigma_X^2=611, mu_Y=347, sigma_Y^2=689  

rho=−0.25  

P(309.2<Y<380.6)  

E(Y∣x)  

Var⁡(Y∣x)  

P(309.2<Y<380.6∣X=385.1)