Answer to Question #316557 in Statistics and Probability for blizzy

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

$i:\\P\left( Y=0 \right) =\frac{C_{8}^{4}}{C_{11}^{4}}=0.212121\\P\left( Y=1 \right) =\frac{C_{8}^{3}C_{3}^{1}}{C_{11}^{4}}=0.509091\\P\left( Y=2 \right) =\frac{C_{8}^{2}C_{3}^{2}}{C_{11}^{4}}=0.254545\\P\left( Y=3 \right) =\frac{C_{8}^{1}C_{3}^{3}}{C_{11}^{4}}=0.0242424\\ii:\\EY=0\cdot 0.2121+1\cdot 0.5091+2\cdot 0.2545+3\cdot 0.2424=1.7453$