Let X has probability density function f(x) = 0·75(1 − x²), x ∈ [−1, 1]; 0 otherwiseमाना कि X में संभाव्यता घनत्व फलन है
Let X has probability density function
f(x) = 0·75(1 − x²), x ∈ [−1, 1]; 0 otherwise
What is the probability of P(−1/2 ≤ X ≤ 1/2)?
माना कि X में संभाव्यता घनत्व फलन है
f(x) = 0·75(1 − x²), x ∈ [−1, 1]; अन्यथा 0
प्रायिकता P(−1/2 ≤ X ≤ 1/2) क्या है?
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Correct answer: (A) 0·680·68
Explanation
P = 0.75 ∫ from −1/2 to 1/2 of (1 − x²) dx = 0.75 (1 − 1/12) = 0.6875, which is about 0.68 (the closest option).P = 0.75 ∫ (−1/2 से 1/2) (1 − x²) dx = 0.75 (1 − 1/12) = 0.6875, जो लगभग 0.68 है (निकटतम विकल्प)।