Question
Download Solution PDFX और Y स्वतंत्र सामान्य चर हैं जिनका माध्य क्रमशः 50 और 80 है और मानक विचलन क्रमशः 4 और 3 है। X + Y का बंटन क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
X और Y स्वतंत्र सामान्य चर हैं जिनके
माध्य (X) = 50
माध्य (Y) = 80
SD (σx) = 4
SD(σy) = 3
अवधारणा:
सामान्य बंटन N(μ, √(σ2x+ σ22)) द्वारा दर्शाया जाता है
गणना
चूंकि X और Y स्वतंत्र हैं तो
⇒ Z = X + Y ~ N(X + Y, (σ2x + σ2y)
⇒ P(Z) = P(X + Y) ~ N(130, (42 + 32)
⇒ N(130, 25)
∴ N(μ, √(σ2x+ σ22), N(130, 5) है।
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