Two balls are chosen randomly from an urn containing 6 red and 4
black balls, without replacement. Suppose that we win $2 for each
black ball selected and we lose $1 for each red ball selected. Let
X denote the amount on money we won or lost.
(a) Find the probability mass function of X, i.e., ﬁnd P(X = k) for all possible values of k.
(b) Compute E[X].
(c) Compute Var(X)
a) below is probability mass function of X :
P(X=-2)=P(both red balls)=(6/10)*(5/9)=1/3
P(X=1)=P(1red and 1 black ball)=2*(6/10)*(4/9)=8/15
P(X=4)=P(both black balls)=(4/10)*(3/9)=2/15
|E(x) =μ=||ΣxP(x) =||0.4000|
|E(x2) =||Σx2P(x) =||4.0000|
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