GATE CS 2021 Set 2 — Question 32
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Engineering Mathematics → Probability & Statistics → Discrete Distributions
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Question
For a given biased coin, the probability that the outcome of a toss is a head is . This coin is tossed times. Let denote the random variable whose value is the number of times that head appeared in these tosses. The standard deviation of (rounded to decimal places) is ________.
Correct answer
15 to 16
Solution
The random variable represents the number of successes in independent Bernoulli trials with success probability . Thus, follows a Binomial distribution: .The variance of a Binomial distribution is calculated as:Substituting the given values:The standard deviation is the square root of the variance:Rounding to two decimal places, the standard deviation is .
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