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1 घंटे की परीक्षा को पूरा करने के लिए एक प्रतियोगिता के एक परीक्षार्थी द्वारा आवश्यक समय (X) एक यादृच्छिक चर है, जिसका प्रायिकता घनत्व फलन \(f(x)=\dfrac{6}{5}(x^2+x);0 \le x \le 1.\) है, तो F(0.5) का मान है:

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SSC CGL Tier-II ( JSO ) 2019 Official Paper ( Held On : 17 Nov 2020 )
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  1. \(\dfrac{4}{5}\)
  2. \(\dfrac{2}{5}\)
  3. \(\dfrac{3}{5}\)
  4. \(\dfrac{1}{5}\)

Answer (Detailed Solution Below)

Option 4 : \(\dfrac{1}{5}\)
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Detailed Solution

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दिया है

F(x) = 6/5(x2 + x); 0 ≤ x ≤ 1

गणना

F(x) = \(\mathop \smallint \nolimits_0^x f\left( x \right)dx\)

⇒ \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qadaqfWaqabSWdaeaapeGaaGimaaWdaeaaieWapeGaa8hEaaqdpaqa % a8qacqGHRiI8aaaaaa!3A60! \mathop \smallint \nolimits_0^x \)6/5(x2 + x)dx

समाकलन के बाद हमें प्राप्त,

⇒ f(0.5) = (6/5)((0.5)3/3 - (0.5)2/2)

⇒ (6/5)(0.25/6 + 0.75/6)

⇒ (6/5)(1/6)

⇒ 1/5

∴ F(0. 5) का मान 1/5 है।

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