3.61 A tobacco company produces blends of tobacco, with each blend containing various proportions of Turkish, domestic, and other tobaccos. The propor- tions of Turkish and domestic in a blend are random variables with joint density function (X = Turkish and Y = domestic) S24.xy, 0

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3.61 A tobacco company produces blends of tobacco,
with each blend containing various proportions of
Turkish, domestic, and other tobaccos. The propor-
tions of Turkish and domestic in a blend are random
variables with joint density function (X = Turkish and
Y = domestic)
S24.xy, 0<x, Y < 1, x+ y < 1,
10,
f(x, y) =
elsewhere.
(a) Find the probability that in a given box the Turkish
tobacco accounts for over half the blend.
(b) Find the marginal density function for the propor-
tion of the domestic tobacco.
(c) Find the probability that the proportion of Turk-
ish tobacco is less than 1/8 if it is known that the
blend contains 3/4 domestic tobacco.
Transcribed Image Text:3.61 A tobacco company produces blends of tobacco, with each blend containing various proportions of Turkish, domestic, and other tobaccos. The propor- tions of Turkish and domestic in a blend are random variables with joint density function (X = Turkish and Y = domestic) S24.xy, 0<x, Y < 1, x+ y < 1, 10, f(x, y) = elsewhere. (a) Find the probability that in a given box the Turkish tobacco accounts for over half the blend. (b) Find the marginal density function for the propor- tion of the domestic tobacco. (c) Find the probability that the proportion of Turk- ish tobacco is less than 1/8 if it is known that the blend contains 3/4 domestic tobacco.
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