Question

Consider the experiment of blindly picking a ball from a box. Let Y be a random variable equal to O when the ball is green, 1 when the ball is red, and 2 when the ball is yellow. There are 50 green balls, 40 red balls, and 10 yellow balls in the box. So that the PrtY-o) 0.50, Pr(Y-1)-0.40, and PrtY-2) 0.10. What is the variance of Y? (Rounded to two decimals.)
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Answer #1

From the given Probability Mass Function of Y, the following Table is formed:

y p yp y2 p
0 0.5 0 0
1 0.4 0.4 0.4
2 0.1 0.2 0.4
Total = 1.0 0.6 0.8

E(Y) = Σ YiPi = 0.6

pi 0.8

Variance of Y is given by:

s2 = E(уг) _ (E(y) )2-0.8-0.62-0.44

So,

Answer is:

0.44

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