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The standard deviation of a uniformly distributed random variable between 0 and 1 is
- a)1/√12
- b)1/√3
- c)5/√12
- d)7/√12
Correct answer is option 'A'. Can you explain this answer?
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Explanation:
Uniform distribution means that all values between 0 and 1 are equally likely to occur. The formula for the standard deviation of a uniform distribution is:
σ = √[(b-a)²/12]
where σ is the standard deviation, a is the lower limit (0 in this case), and b is the upper limit (1 in this case).
Substituting the values in the formula, we get:
σ = √[(1-0)²/12] = √(1/12) = 1/√12
To simplify further, we can rationalize the denominator by multiplying and dividing by √3:
σ = 1/√12 x √3/√3 = √3/√36 = √3/6
Finally, we can simplify this further by dividing both numerator and denominator by 2:
σ = √3/6 ÷ 2/2 = √3/12
Therefore, the correct answer is option 'A' which is 1/12.
Uniform distribution means that all values between 0 and 1 are equally likely to occur. The formula for the standard deviation of a uniform distribution is:
σ = √[(b-a)²/12]
where σ is the standard deviation, a is the lower limit (0 in this case), and b is the upper limit (1 in this case).
Substituting the values in the formula, we get:
σ = √[(1-0)²/12] = √(1/12) = 1/√12
To simplify further, we can rationalize the denominator by multiplying and dividing by √3:
σ = 1/√12 x √3/√3 = √3/√36 = √3/6
Finally, we can simplify this further by dividing both numerator and denominator by 2:
σ = √3/6 ÷ 2/2 = √3/12
Therefore, the correct answer is option 'A' which is 1/12.
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The standard deviation of a uniformly distributed random variable between 0 and 1 isa)1/√12b)1/√3c)5/√12d)7/√12Correct answer is option 'A'. Can you explain this answer?
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