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Consider a binomial random variable X. If X1 ,X2 ....., X n are independent and identically distributed samples from the distribution of X with sum then the distribution of Y as n → ∞ can be approximated a
- a)Normal
- b)Bernoulli
- c)Binomial
- d)Exponential
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Consider a binomial random variable X. If X1 ,X2 ....., X n are indepe...
The distribution of Y as n approaches infinity is approximately a normal distribution.
This is known as the Central Limit Theorem, which states that the sum (or average) of a large number of independent and identically distributed random variables will be approximately normally distributed, regardless of the underlying distribution of the individual variables.
In the case of a binomial random variable, where each X_i can take on values of 0 or 1 with a certain probability of success p, the sum of these variables will represent the total number of successes out of n trials. As n gets larger, the distribution of Y will approach a normal distribution with mean np and variance np(1-p).
This is known as the Central Limit Theorem, which states that the sum (or average) of a large number of independent and identically distributed random variables will be approximately normally distributed, regardless of the underlying distribution of the individual variables.
In the case of a binomial random variable, where each X_i can take on values of 0 or 1 with a certain probability of success p, the sum of these variables will represent the total number of successes out of n trials. As n gets larger, the distribution of Y will approach a normal distribution with mean np and variance np(1-p).
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Consider a binomial random variable X. If X1 ,X2 ....., X n are indepe...
The distribution of Y as n → ∞ can be approximated a Normal.
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Consider a binomial random variable X. If X1 ,X2 ....., X n are independent and identically distributed samples from the distribution of X with sum then the distribution of Y as n → ∞ can be approximated aa)Normal b)Bernoullic)Binomiald)ExponentialCorrect answer is option 'A'. Can you explain this answer?
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