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GATE 2021 ME (ME2) – Question 13

Engineering Mathematics · Probability and Statistics: Mean, median, mode, standard deviation, random variables and distributions · 1 mark · Multiple choice

The mean and variance, respectively, of a binomial distribution for n independent trials with the probability of success as p, are

  1. $\sqrt{np},np(1-2p)$
  2. $\sqrt{np},\sqrt{np(1-p)}$
  3. $np,np$
  4. $np,np(1-p)$

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Show answer and explanation

Correct answer: (D) $np,np(1-p)$

Explanation

Write the count as a sum of n independent Bernoulli indicators. Each has mean p and variance p(1−p).

Means and independent variances add, giving **np and np(1−p), D**. The square root of variance is standard deviation, not variance.