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Part BCSIR NET June 2024the-two-pieces-are-not-independent

The two pieces are not independent

Let a point P be chosen at random on the line segment AB of length α\alpha. Let Z1Z_{1} and Z2Z_{2} denote the lengths of line segments AP and BP respectively. Then the value of E(|Z1−Z2Z_{1} - Z_{2}|) is

  1. A.α\alpha
  2. B.2α2\alpha
  3. C.α/2\alpha/2✓ Correct
  4. D.2α/32\alpha/3

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests dependence misread.

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50 are analysed free — try those first.

The trap it tests

Dependence misread

Independence, pairwise vs mutual, or correlation vs dependence.

Drill statements like this

Related counterexample: If X and Y are each normal and uncorrelated then they are independent

More on this topic

The chapter behind this: Joint distributions, transformations and order statistics — free to read

From Probability › Joint distributions, transformations, order statistics

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