A jar contains 25 red balls, 15 green balls, and 10 white balls. Twelve balls are selected with replacement. Let Y₁ be the number of red balls selected, Y₂ the number of green balls selected, and Y₃ the number of white balls selected.

Find (a) p(7, 3, 2), (b) E(Y₂), (c) V (Y₃), (d) Cov(Y₁, Y₂), (e) the correlation coefficient for Y₁ and Y₃. (f) If U is the number of green or white balls selected, find the correlation coefficient of Y₁ and U.

Ans. (a) 0.066825 (b) 3.6 (c) 1.92 (d) 1.8 (e) .65465 (f) 1