Question

A store donated a lot of 8 computer sets that includes 3 which are malfunctioning or defective. If 4 of this computer sets are chosen at random for delivery to a school.

i) What will be the probability mass function of a random variable 𝑌?

ii) What will be the expected value of 𝑌?

Answer 1

$i:\\P\left( Y=0 \right) =\frac{C_{5}^{4}}{C_{8}^{4}}=0.0714286\\P\left( Y=1 \right) =\frac{C_{5}^{3}C_{3}^{1}}{C_{8}^{4}}=0.428571\\P\left( Y=2 \right) =\frac{C_{5}^{2}C_{3}^{2}}{C_{8}^{4}}=0.428571\\P\left( Y=3 \right) =\frac{C_{5}^{1}C_{3}^{3}}{C_{8}^{4}}=0.0714286\\ii:\\EY=1\cdot 0.428571+2\cdot 0.428571+3\cdot 0.0714286=1.5$