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

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QUESTION 1 [13 MARKS]
Write down only the letter corresponding to your choice next to
the question number.
1.1. A random variable that can assume only a finite number of
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b) Finite sequence
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