Question

please explain as much as possible, thanks

An instructor has given a short quiz consisting of two parts. For a randomly selected student, let X = the number of points earned on the first part and Y = the number of points earned on the second part. Suppose that the joint pmf of X and Y is given in the accompanyin y p(x,y) 0 5 10 15 0 0.01 0.06 0.02 0.10 5 0.04 0.13 0.20 0.10 10 0.01 0.15 0.17 0.01 (a) If the score recorded in the grade book is the total number of points earned on the two parts, what is the expected recorded score E(X + Y)? (Enter your answer to one decimal place.) (b) If the maximum of the two scores is recorded, what is the expected recorded score? (Enter your answer to two decimal places.)

Answer 1

The given joint pmf is Y blacy) 15 5. 10 X 5 Lool 0.06 0.02 0.10 10.04 0.13 0.20 0.10 Tool 0.15 0.17 0.0) 10 2 (a) If score recorded is xty then the expected earned score will be - 11 E(X+Y) E (X+Y): $1264) slo+0110.01)+10+5) 10.06) + (10)(0:02)+(15)10:1) +(5)(0.04) + (10)[0:13) +115)10.2) + (20)(0:1) +(10)10:01)+15(0:15) + 2010.17) +2510.01) - 14.5 edici cortudjetoih Hence, E(X+Y) - 14.5 Ans ebrund 6 (b) of maximum of two scores is recorded, the expected earned score will be (mar(x, y)) - {(max(x,y)) .placy) clo)10.01) +540.06)+lolo.02) + 15(0:1)+510:04)+5(0:13) +10(0.2) +1510:1)+ 1020.01 ) +10(0.15) + 1010:17) +15 10.0)) a -9.8 Hence, sə Elmax (x, y)) =9.8 Ang.

Hence the required answers to the given questions are-

a) 14.5

b) 9.8