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An unbiased coin tossed 3times find the expected value of the number of heads and also it's standard deviation?
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An unbiased coin tossed 3times find the expected value of the number o...
Expected Value of Number of Heads
Standard Deviation
Explanation
- When a coin is tossed, the probability of getting a head is 0.5
- Therefore, the probability of getting a tail is also 0.5
- Since the coin is unbiased, the probability of getting a head or tail is the same for each toss
- The expected value of the number of heads in one toss is therefore 0.5
- For three tosses, we can use the formula E(X) = np, where n is the number of trials and p is the probability of success
- In this case, n = 3 and p = 0.5
- E(X) = 3 x 0.5 = 1.5
- Therefore, the expected value of the number of heads in three tosses is 1.5
Standard Deviation
- The formula for standard deviation is σ = sqrt(np(1-p))
- Using the values of n = 3 and p = 0.5, we get σ = sqrt(3 x 0.5 x 0.5) = 0.866
- Therefore, the standard deviation of the number of heads in three tosses is 0.866
Explanation
- The expected value of the number of heads in three tosses is the average number of heads that we can expect to get over a large number of trials
- We calculate this by multiplying the probability of getting a head in one toss by the number of tosses
- The standard deviation tells us how spread out the distribution of the number of heads is
- A smaller standard deviation means that the values are closer together and a larger standard deviation means that the values are more spread out
- In this case, the standard deviation is relatively small, which means that we can expect to get the same number of heads in each trial
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An unbiased coin tossed 3times find the expected value of the number of heads and also it's standard deviation?
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An unbiased coin tossed 3times find the expected value of the number of heads and also it's standard deviation? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about An unbiased coin tossed 3times find the expected value of the number of heads and also it's standard deviation? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An unbiased coin tossed 3times find the expected value of the number of heads and also it's standard deviation?.
An unbiased coin tossed 3times find the expected value of the number of heads and also it's standard deviation? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about An unbiased coin tossed 3times find the expected value of the number of heads and also it's standard deviation? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An unbiased coin tossed 3times find the expected value of the number of heads and also it's standard deviation?.
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