Question

Please answer both questions.

Thanks.

0/0.31 points Previous Answers DevoreStat9 5.E.022 2. My Notes Ask Your Teacl 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 accompanying table. y P(x, у) 0 5 10 15 0 0.02 0.06 0.02 0.10 0.04 0.15 5 0.20 0.10 X 0.01 0.15 10 0.14 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.) 0.5 X (b) If the maximum of the two scores is recorded, what is the expected recorded score? (Enter your answer to two decimal places.) 0/0.31 points | Previous Answers DevoreStat9 5.E.030 3. My Notes Ask Your Teac 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 accompanying table. p(x, y) 0 10 15 O 0.01 0.06 0.02 0.10 5 0.04 0.13 0.20 0.10 X 10 0.01 0.15 0.17 0.01 (a) Compute the covariance for X and Y. (Round your answer to two decimal places.) -0.24 Cov(X, Y (b) Computep for X and Y. (Round your answer to two decimal places.) = -0.25

Answer 1

Given jaint pmf is Y 15 O.10 0.06 O.2 O.02 O.02 O.49 X O15 O.10 0.04 . 20 0.01 O.3 O.14 0.15 JO O-21 O.36 PCy) O.36 O.07 Xis Ma1ginal pmt of X o.49 P (x) .31 2 af 1 is, morginal pmf 15 O.36 0 21 d.36 PLy) O.07 (l0x0.31) 0 (5 X0.49+ Elx) 5.55

27ypy) E(4) (5x0.36)+ (tox0 36)+ (15 xo.21) E(M) 8.55 E(x)+ E(Y) al E (Xt4) . . 5.55+8.55 E (xt 4) 14. 2=Max (X,Y O.02 T O2 i o 10 Ot0 15 15 0.04 o.15 15 55 O 20 lo O10 I5 15 o.ol ld 10 0-15 T O.14 10 lo a.0 15 15 2 Max(X7Y is, PMf of 15 1O.e 10 a.2) P/2) 0.02 0.25 52 E() 2 2 P/2 (5 x0.25) +(10x0.52) +15X0.21) E (2) g.6

Expected Tecosded scoe 9.60 Given: pixt P(e) 15 O O.06 O.o1 O.19 O 02 X 5 O.04 0.13 O20 O.47 d.10 10 O.15 O.34 d.of PCY) 0.34 0.39 0.21 dTo Compute Cou(x,y) flarginal pmf of isy 10 Pla) O.19 O.47 O 34 Maiginal Yis pmf of 15 lo O 4 0 39 O.2 (X1# 0.34 4.06 Cou (X4) F (X)- E(X) .ECY 2 2 E(XY) (5*5KO13)t (SXIOXO.20) + (10 X5X0.15)+ (5x 15 X0-10)+(X15 x .01)t (1oxI0xo-11) tan t lerix Ce) 3.25+ 10 7.5+7.5+ 5+ 17 46.75 E (X4) xp(R) E (x) + (1ox0.34) (5x0.47) 5.75 E (X)

E (4)= (5 x0.34)+ ClOxo 39)t C15x0.21 t 7 3.9 + 3.15 E(1) (5.75X8.75 46.75- Cou (X) LCou (x -3-562 5 Κoν (x.y) - 3.56 . 1 e for (x,) Cov (X,) - E (x)-IE (X)1 V(x)= (572 x0.47 t Cio xo.34 E(x) 45.75 45.75 V (X) (5.75)2 12-6875 E(Y)-E( E() (5) x6.34) (1o x0.39) t (15)l xo - 34.15 l EC) T V(Y) g4.75-(8.75) V(Y) 18-1815 1419 ..

3-56 12-6875 18-1375 -0.23