मान लीजिए X औसत शून्य और भिन्नता 9 के साथ एक सामान्य यादृच्छिक चर है। यदि a = P(X ≥ 3) है, तो P(|X| ≤ 3) किसके बराबर है?

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  1. 1 - 2a
  2. 1 - a
  3. 2a
  4. a

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Option 1 : 1 - 2a
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DSSSB TGT Social Science Full Test 1
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सही उत्तर विकल्प 1 है।

आकड़े:

औसत = μ = 0;

भिन्नता = σ2 = 9 

P(X ≥ 3) = a

गणना:

मानक विचलन = σ = √भिन्नता = √9 = 3

P(|X| ≤ 3) = P(-3 ≤ X ≤ 3)

P(-∞ ≤ X ≤ +∞) = P(X ≤ 3) + P(-3 ≤ X ≤ 3) + P(X ≥ 3) = 1

चूँकि यह z = 1 के साथ एक सामान्य वितरण है। 

P(X ≥ 3) = P(X ≤ 3) = a

 P(X ≤ 3) + P(-3 ≤ X ≤ 3) + P(X ≥ 3) = 1

a + P(|X| ≤ 3) + a = 1

∴ P(|X| ≤ 3) = 1 - 2a

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