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])2 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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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.
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Overall, R can be greater than, equal to, or less than 0 depending on the variance of the random variable x.