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If all the values taken by a random variable are equal then
- a)its expected value is zero
- b)its standard deviation is zero
- c)its standard deviation is positive
- d)its standard deviation is a real number
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If all the values taken by a random variable are equal thena)its expec...
Explanation:
A random variable is a variable whose possible values are numerical outcomes of a random phenomenon. If all the values taken by a random variable are equal, then the variable is a constant random variable.
a) its expected value is zero: Since all the values are equal, the expected value will be the same as those values. Therefore, the expected value will be the constant value itself, which is not zero in general.
b) its standard deviation is zero: The standard deviation of a random variable is a measure of the spread of its values. Since all the values are equal, there is no spread, and the standard deviation is zero.
c) its standard deviation is positive: This option is incorrect since the standard deviation cannot be positive if all the values are equal.
d) its standard deviation is a real number: This option is incorrect since every real number is a real number, and it does not provide any useful information.
Therefore, the correct answer is option B.
A random variable is a variable whose possible values are numerical outcomes of a random phenomenon. If all the values taken by a random variable are equal, then the variable is a constant random variable.
a) its expected value is zero: Since all the values are equal, the expected value will be the same as those values. Therefore, the expected value will be the constant value itself, which is not zero in general.
b) its standard deviation is zero: The standard deviation of a random variable is a measure of the spread of its values. Since all the values are equal, there is no spread, and the standard deviation is zero.
c) its standard deviation is positive: This option is incorrect since the standard deviation cannot be positive if all the values are equal.
d) its standard deviation is a real number: This option is incorrect since every real number is a real number, and it does not provide any useful information.
Therefore, the correct answer is option B.
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If all the values taken by a random variable are equal thena)its expec...
Standard deviation ia measure of dispersion. All the measures of dispersion will tell us how much each value in a sample is deviating from its mean. When all the expected values are same, then the mean will be that repeating value. As there is no deviation, standard deviation will be zero
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