एक द्विपद बंटन में, यदि माध्य 6 है और मानक विचलन √2 है, तो क्रमशः प्राचल n और p के मान क्या हैं?

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NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. 18 और 1/3
  2. 9 और 1/3
  3. 18 और 2/3
  4. 9 और 2/3

Answer (Detailed Solution Below)

Option 4 : 9 और 2/3
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व्याख्या:

दिया गया है:

⇒ माध्य x = np = 6....(i)

मानक विचलन = \(\sqrt{npq} = \sqrt2\)...(ii)

(ii) को (i) से विभाजित करने पर, हमें प्राप्त होता है

\(\frac{npq}{np} = \frac{2}{6}\)

⇒ q= 1/3

अब

⇒ p = 1 - q = 1- 1/3 = 2/3

(i) से

\(n\times \frac{2}{3} = 6\)

⇒n =9

∴ विकल्प (d) सही है।

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