Q1 Forty students were given two tests– one in Mathematics and second in Statist

Question

Q1

Forty students were given two tests– one in Mathematics and second in Statistics with twoquestions each – Let X is the number of questions astudent answered correctly in Maths test and Y the number ofquestions a student answered correctly in Statistics test.

find:

                    i.      The joint probability distributionof X and Y.

                  ii.      Marginal probabilitydistributions of X and Y.

                 iii.      Expected values of the twomarginal probability distributions.

Explanation / Answer

(i) The joint probability distribution of X and Y is XY 0 1 2 P(X) 0 0.05 0.075 0.025 0.15 1 0.125 0.175 0.2 0.5 2 0.025 0.225 0.1 0.35 P(Y) 0.2 0.475 0.325 1 (ii) Marginal probability distributions of X is     X        0      1        2 P(X)   0.15   0.5    0.35 Marginal probability distributions of Y is      Y     0         1        2 P(Y)   0.2 0.475 0.325 (iii) Expected values of the two marginal probability distributionsare E(X)=0*0.15+1*0.5+2*0.35=1.2 E(Y)=0*0.2+1*0.475+2*0.325=1.125

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.