मना कि X एक मानक सामान्य वितरण है। E (X3) 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. \((t^3+3t)e^{\frac{t^2}{2}}\)
  2. \(t^3e^{\frac{t^2}{2}}\)
  3. \(e^{\frac{t^2}{2}}\)
  4. 0

Answer (Detailed Solution Below)

Option 4 : 0
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व्याख्या

सामान्य वितरण का प्रायिकता वितरण फलन हमें इस प्रकार दिया गया था:

⇒ F(x) =[1/σ√2π ]e-(x – μ)2/2σ2

यदि हम Z = (x - μ)/σ को सामान्य वितरण में रखते हैं तो इसे मानक सामान्य वितरण कहते हैं।

मानक सामान्य वितरण का प्रायिकता वितरण फलन इस प्रकार है।

⇒ f(x) = [1/σ√2π]e- z^2/2

एक मानक सामान्य वितरण में  E(X3) का मान 0 है।

 

सामान्य वितरण का मानक विचलन = σ = 1

सामान्य वितरण का विषमता गुणांक β1 = 0 है।

सामान्य वितरण में कर्टोसिस गुणांक β3 = 3 है।
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