GATE CSE 2021 Set 2 | Question: 22

Question

For a given biased coin, the probability that the outcome of a toss is a head is $0.4$. This coin is tossed $1,000$ times. Let $X$ denote the random variable whose value is the number of times that head appeared in these $1,000$ tosses. The standard deviation of $X$ (rounded to $2$ decimal place) is _________

Answer 1

It is Independent trails with same rate of success. So we can use Binomial distribution

Probability of success $(p) = 0.4$

Probability of failure $(q) = 1 – 0.4 = 0.6$

Number of trials $(n) = 1000$

Variance $=n\times p\times q = 1000 * 0.4 * 0.6 = 240$

Standard deviation $=\sqrt{240} = 15.49$

Comments

For a given biased coin, the probability that the outcome of a toss is a head is 0.4 . This coin is tossed 1, 000 times. Let X denote the random variable whose value is the number of times that head appeared in these 1, 000 tosses. The standard deviation of X (rounded to 2 decimal place) is

This line doesn’t affect the answer.??

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@ASNR1010 Here $success(p)$ is taken as appearance of head in a toss. The answer is accordingly written.