calculated the following probability mass function using the information on gend

Question

calculated the following probability mass function using the information on gender (male X = Female X = 1) and student level (undergraduate Y = 0, graduate Y = 1) from NIU. Answer the following with the information provided. a. what is the probability a person was male and was an undergraduate P(X = 0, Y = 0)? b. Calculate the marginal probability mass functions of males X- 0 and females X can put your answer in margins of the table. c. Calculate the marginal probability mass functions of undergraduates Y = 0 and graduate Y = 1. You can put your answer in the margins of the table. d. Calculate the covariance of the joint probability mass function. The shortcut is easier to calculate Cov(X, Y) = E(XY) - mu_x mu_Y e. Calculate the correlation coefficient with V(X) = 0.25 and V(Y) = 0.1875. The correlation equation is rho_x, y = = Cov(X, Y)/sigma_X sigma_Y.

Explanation / Answer

a)P(X=0,Y=0) =0.38

b)from above tabl;e

hence marginal density of X:

c) similarly marginal density of y:

d)here E(X)=1*0.5=0.5

and E(Y)=1*0.25=0.25

E(XY)=1*0.13 =0.13

hence Covar(X,Y) =0.13-0.25*0.5 = 0.005

e) correlation coefficient =0.005/(0.25*0.1875)1/2 =0.0231

y x 0 1 Total 0 0.38 0.12 0.5 1 0.37 0.13 0.5 Total 0.75 0.25 1

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