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The graph of the probability density function of a random variable X is shown below. What should be the value of λ for this probability density function to be valid?
  • a)
    2/3
  • b)
    1/3
  • c)
    1
  • d)
    3/4
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The graph of the probability density function of a random variable X i...
Concept:
We know, for valid PDF :
Calculation:
The graph of the pdf is given in triangular form with the base length as 3 and the height as λ.
We know, for valid PDF :
The above is representing the area under the curve between x ϵ [-2, 1].
⇒ 1/2 (base) × Height = 1 
⇒ 1/2 (1- (-2)) × λ = 1 
⇒ λ = 2/3
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