Question

Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable—X for the right tire and Y for the left tire, with joint pdf given below.

f(x, y) =

K(x^{2} + y^{2}) |
22 ≤ x ≤ 32, 22 ≤ y ≤ 32 | |

0 | otherwise |

(a) Compute the covariance between *X* and
*Y*.

(b) Compute the correlation coefficient *p* for this
*X* and *Y*.

Answer #1

E(X)= xf(x,y) dx =27.3052 =E(Y)

V(X)=
(x-E(x))^{2} f(x,y) dx =8.2779

E(XY)= xyf(x,y) dx =27.3052 =745.4783

a)

covariance between *X* and *Y*
=Cov(X,Y)=E(XY)-E(X)*E(Y)**=-0.0931**

**b)** correlation coefficient *p* for this
*X* and *Y*
=Cov(X,Y)/sqrt(Var(X)*Var(Y))**=-0.0112**

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