Question
Download Solution PDFनिरंतर यादृच्छिक चर X की अन्तःचतुर्थक परास जिसका प्रायिकता घनत्व फलन f(x) = e-x; x ≥ 0 है:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया है
F(x) = e-x
गणना
\(Q_3=\displaystyle\int^{Q_3}_0e^{-x}dx=\dfrac{75}{100}\) के लिये
⇒ ¾ = (-e-x)Q30
⇒ ¾ = (-1 – e-Q3)
⇒ ¼ = e-Q3
⇒Q3 = In 4
\(Q_1=\displaystyle\int^{Q_1}_0e^{-x}dx=\dfrac{25}{100}\) के लिये
⇒ (-e-xdx)Q10 = 1/4
⇒ (- 1 – e-Q1) = ¼
⇒ Log Q1 = ¾
Q1 = In 4/3
⇒ अन्तःचतुर्थक परास = Q3 – Q1
⇒ In 4 – In 4/3
⇒ In 4 –(In 4 – In 3)
∴ अन्तःचतुर्थक परास In 3 है।
प्रायिकता घनत्व फलन = \(\displaystyle\int_0^\infty f(x)\ dx=1\)
Last updated on Jul 10, 2025
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