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If the difference between the expectation of the square of a random variable (E[x2] and the square of the expectation of the random variable (E[x])2 is denoted by R, then

  • a)
    R = 0

  • b)
    R < 0

  • c)
    R ≥ 0

  • d)
    R > 0

Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If the difference between the expectation of the square of a random va...
Random variable assigns a real number to each possible outcome.


Let X be a discreet random variable,then




where V(x) is the variance of x,


Explanation:



  • The difference between the expectation of the square of a random variable (E[X2]) and the square of the expectation of the random variable (E[X])2 is called the variance of a random variable

  • Variance measure how far a set of numbers is spread out

  • A variance of zero(R=0) indicates that all the values are identical




  • A variance of X = R =E[X2]- (E[X])This quantity is always non-negative as it is an expectation of a non-negative quantity

  • A non-zero variance is always positive means R > 0



So, R ≥ 0 is the answer. Since variance is  and hence never negative, 
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Most Upvoted Answer
If the difference between the expectation of the square of a random va...
Is always greater than 0c)R is always less than 0d)R can be greater than, equal to, or less than 0

The correct answer is d) R can be greater than, equal to, or less than 0.

The expression E[x^2] - (E[x])^2 is known as the variance of the random variable x, denoted by Var(x) or σ^2. The variance measures the spread or dispersion of the random variable.

If Var(x) = 0, it means that x has zero variance and is a constant, meaning there is no spread or variability in the values x can take. In this case, R would be equal to 0.

If Var(x) > 0, it means that x has non-zero variance and there is some spread or variability in the values x can take. In this case, R would be greater than 0.

If Var(x) < 0,="" it="" would="" imply="" that="" the="" variance="" is="" negative,="" which="" is="" not="" possible="" because="" variance="" is="" always="" non-negative.="" therefore,="" r="" cannot="" be="" less="" than="" />

Overall, R can be greater than, equal to, or less than 0 depending on the variance of the random variable x.
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If the difference between the expectation of the square of a random variable (E[x2] and the square of the expectation of the random variable (E[x])2 is denoted by R, thena)R = 0b)R < 0c)R ≥ 0d)R > 0Correct answer is option 'C'. Can you explain this answer?
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If the difference between the expectation of the square of a random variable (E[x2] and the square of the expectation of the random variable (E[x])2 is denoted by R, thena)R = 0b)R < 0c)R ≥ 0d)R > 0Correct answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about If the difference between the expectation of the square of a random variable (E[x2] and the square of the expectation of the random variable (E[x])2 is denoted by R, thena)R = 0b)R < 0c)R ≥ 0d)R > 0Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the difference between the expectation of the square of a random variable (E[x2] and the square of the expectation of the random variable (E[x])2 is denoted by R, thena)R = 0b)R < 0c)R ≥ 0d)R > 0Correct answer is option 'C'. Can you explain this answer?.
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