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GATE 2025 · session-5
Probability and StatisticsBernoulli DistributionmediumMCQ2 marks
A random variable \( X \) is said to be distributed as \( Bernoulli(\theta) \), denoted by \( X \sim Bernoulli(\theta) \), if \[ P(X = 1) = \theta, \quad P(X = 0) = 1 - \theta \] for \( 0 < \theta < 1 \). Let \( Y = \sum_{i=1}^{300} X_i \), where \( X_i \sim Bernoulli(\theta) \), \( i = 1, 2, \dots, 300 \) be independent and identically distributed random variables with \( \theta = 0.25 \). The value of \( P(60 \leq Y \leq 90) \), after approximation through the Central Limit Theorem, is given by
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