.0000 Ultra 11:20 PM CON420ProjectFall Open with Print ECON 420 Statistios Puoje

Question

.0000 Ultra 11:20 PM CON420ProjectFall Open with Print ECON 420 Statistios Puoject Due Date Tuesday, 09.24 We ase nterested to undeetand the ilationship between the stock price of a listed company and the SdclP500 Index We eolect prices for the bwo asects from YahooFinane we fin t matr the ntensofthe sbxk and the ink, where the Ntam defined hmasthe peromtagr changy We then create the following two variahles equal to 1 if the stock reterm in day t is larger or equal to ero, and equal to 0 the kneturm was negative X: equal to 1 if the market seturn in day t is langer or equal to aen, and equal to D if the m was negtive The jpint peebalklity disteibution femction of X and Y is given in the llowing Talle Answer the following questions . What dees each umber in the lour oels represent? h.Cakulate the marginal distrbution of X and Y Caulate the probability destribuition function oll Y conditional on X-0and X-1 Are Xand Y independon justsify your statement

Explanation / Answer

(a)

The table shows the joint pdf of X and Y. The cell P(X=0, Y=0) = 0.307 shows that both stocks gave return less than zero on day t.

The cell P(X=0, Y=1) = 0.167 shows that stock X gave return less than zero and Y gave positive return on day t.

The cell P(X=1, Y=0) = 0.179 shows that stock X gave positive return and Y gave negative return on day t.

The cell P(X=1, Y=1) = 0.347 shows that both stocks X and Y gave positive return on day t.

(b)

Following table shows the marginal pdf of X and Y:

(c)

Following table shows the conditional pdf:

(d)

Since for each X and Y , follwoing is the not true

P(X=x,Y=y) = P(X=x)P(Y=y)

so X and Y are not independent.

Y 0 1 P(X=x) X 0 0.307 0.167 0.474 1 0.179 0.347 0.526 P(Y=y) 0.486 0.514 1

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