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UGC NET CSE | June 2014 | Part 2 | Question: 37

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A text is made up of the characters $\alpha, \beta, \gamma, \delta$ and $\sigma$ with the probability $0.12, 0.40, 0.15, 0.08$ and $0.25$ respectively. The optimal coding technique will have the average length of 

  1. $1.7$
  2. $2.15$ 
  3. $3.4$
  4. $3.8$ 
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Answer : B
Alpha=.12      Beta=.40      Gamma=.15      Delta=.08      Sigma=.25     (All are given in question)
Path length with 4= Alpha, Delta. (.48+.32)
Path length with 3= gamma.(.45).
Path length with 2=sigma..(.50).
Path length with 1= beta(.40).
Average path length=2.15 .

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We arrange the characters in ascending order according to its Probabilities

So the path length of   α=4, β=1,γ=3,δ=4 and  σ=2

The optimal path length =(4x0.12)+(1x0.40)+(3x0.15)+(4x0.08)+(2x0.25)

i.e 2.15

hence ans is B

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