Density function for continuous random variables

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SUMMARY

The density function for the continuous random variable Y is defined as f(y) = cy² for the interval 0 ≤ y ≤ 2, and 0 elsewhere. The correct value of c is determined through the definite integral of the function from 0 to 2, yielding c = 3/8. The discussion highlights a discrepancy with a textbook answer of c = 1/8, which is identified as an error. The consensus among participants is that the book's solution is incorrect.

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  • Understanding of continuous random variables
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  • Familiarity with definite integrals
  • Basic calculus skills
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cue928
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For the density function for random variable Y:
f(y) = cy^2 for 0<= y <= 2; 0 elsewhere
We are asked to find the value of c. I did a definite integral from 0 to 2 of cy^2. I get c = 3/8. Why would the book show an answer of c = 1/8? Is this an error on their part or am I missing something stupid?
 
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Indeed, I also think it's an error in the book.
 

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