Question
Download Solution PDFएक यादृच्छिक चर X पर विचार करें जो मापदंडों n = 10 और
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
द्विपद वितरण:
पैरामीटर n और p के साथ P(X = r) के लिए द्विपद वितरण निम्नानुसार दिया गया है:
जहाँ q पूरक घटना है।
साथ ही, किसी भी यादृच्छिक चर X का गुण,
E(aX + b) = aE(X) + b
V(aX + b) = (a2)V(X)
गणना:
दिया गया है: n = 10 और
इसलिए, q = 1 - p
यादृच्छिक चर X के लिए,
माध्य = E(X) = np = 10 × (1/5) = 2
प्रसरण = V(X) = npq = 10 × (1/5) ×(4/5) = 8/5
चूँकि, Y = 10 - X
⇒ E(Y) = E(10 - X)
⇒ E(Y) = 10 - E(X) = 10 - 2
⇒ 8 = n'p' ....(1)
साथ ही, V(Y) = V(10 - X) = 0 + (-1)2 V(X)
⇒ 8/5 = n'p'q' ....(2)
1 और 2 को हल करने पर हमें n', p', और q' प्राप्त होगा जो होगा,
⇒ 8/5 = 8'q'
⇒ q' = 1/5
⇒ p' = 4/5
अब,
⇒ 8 = n' (4/5)
⇒ n' = 10
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