12. A distributor of fruit basket is going to put 4 apples, 6 oranges and 2 bunc
ID: 3356550 • Letter: 1
Question
12. A distributor of fruit basket is going to put 4 apples, 6 oranges and 2 bunches of grapes in his small gift basket. The weights, in ounces, of these items are the random variables Xi, X2 and X3 respectively with means and standard deviation given in the table below Apples Oranges Grapes Mean ()8 10 7 SD (o 0.91.1 Find the mean, variance and standard deviation of the random variable Y, which is weight of fruit in a small gift basket. Assume the weights of different types of fruits are independent (a) E(Y) = 104 ; Var(Y) = 78.49 ; SD (Y) = 5.8959 (b) E(Y) = 88 ; Var(Y) = 42.82 ; SD (Y) = 3.1257 (c) E(Y) = 106 ; Var(Y) = 72.52 ; SD (Y) = 8.5159 (d) E(Y) = 120 ; Var(Y) = 82.72 ; SD (Y) = 9.2316Explanation / Answer
Y = 4X1 + 6X2 + 2X3
E(Y) = 4*E(X1) + 6*E(X2) + 2*E(X3)
= 4*8 + 6*10 + 2*7
= 106
V(Y) = 42 * V(X1) + 62 * V(X2) + 22 * V(X3)
= 16 * 0.92 + 36 * 1.12 + 4 * 22
= 72.52
Sd(Y) = sqrt(72.52) = 8.5159
Option-C) is the correct answer
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