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The probability density function of a random variable X is f(x) = \(\dfrac{\pi}{10} sin \dfrac{\pi x}{5}\); 0 ≤ x ≤ 5. The first quartile of X is:
1. \(\dfrac{10}{3}\)
2. 1
3. \(\dfrac{1}{5}\)
4. \(\dfrac{5}{2}\)

1 Answer

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Best answer
Correct Answer - Option 2 : 1

Calculation:

∫f(x)dx

∫π/10 (sinπx/5)   dx

let πx/5 = t

πdx/5 = dt

dx = 5dt/π

∫.π/10  sint × 5dt/π

 (−1/2)[cost]

= 1

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