Question

In a factory, computer hard drives are collected in boxes containing 40 hard drives each. A box has 6 defective hard drives, and 34 hard drives which are not defective. A quality control inspector randomly selects 3 hard drives in that box. Consider the discrete random variable X defined as the number of defective hard drives the inspector selects. Find the probability mass function pX of X. Sketch the corresponding cumulative distribution function F

Answer 1

The probability of selecting x defective hard drives is computed here as:
P(X = x) = Number of ways to select x defective ones from 6 defective ones * Number of ways to select (3 - x) non defective ones from 34 non defective ones / Total ways to select 3 hard drives from 40

Therefore the PDF for X now is computed here as:

This is the required probability mass function of X here.

The corresponding cumulative distributive function for X is obtained here as:

P(X <= 0) = 0.6057
P(X <= 1) = 0.9464
P(X <= 2) = 0.9980
P(X <= 3) = 1