0
Var[a(X^2)+b] = E[ ( a(X^2) + b - (aE[X^2] + b ) )^2 ]
= E[ ( a(X^2) + b -aE[X^2] - b )^2 ]
= E[ ( a(X^2) - aE[X^2] )^2]
= E[ (a^2) ( (X^2) -E[X^2] )^2 ]
= E[ ( (X^2) - E[X^2] ) ( (X^2) - E[X^2] ) ]
= (a^2) E[ (X^4) -2(X^2)E[X^2] + ( E[X^2] )^2]
= (a^2) { E[X^4] -2E[X^2]E[X^2] + ( E[X^2] )^2 }
= (a^2) { E[X^4] -2( E[X^2] )^2 + ( E[X^2] )^2 }
= (a^2) { E[X^4] - ( E[X^2] )^2 }
= (a^2) Var[X^2]
*however, we still do not know what Var[X^2] is....
What else can I help you with?
What does Hartley's test measure?
Equal Variance
What is 3m x 3m in square meters?
9m² or 9 square meters or 9 meters squared
Standard costs are used to measure?
price and quantity variance
What is the formula to calculate kinetic energy?
The formula to calculate kinetic energy is KE = 0.5 * m * v^2, where KE represents kinetic energy, m is the mass of the object in motion, and v is the velocity of the object. The formula shows that kinetic energy is directly proportional to the mass of the object and the square of its velocity. This means that an increase in either mass or velocity will result in a corresponding increase in kinetic energy.
What is 1 mile squared in meters squared?
1 miles in metres 1 miles = 1609.344 metres
Is variance based on deviations from the mean?
Variance is the squared deviation from the mean. (X bar - X data)^2
Is the variance of a group of scores the same as the squared standard deviation?
The standard deviation is defined as the square root of the variance, so the variance is the same as the squared standard deviation.
What is the sum of squared deviation?
The variance.
Can variance be negative?
Since Variance is the average of the squared distanced from the mean, Variance must be a non negative number.
What is the variance of a standard deviation of 12.4?
Variance is std dev squared. Therefore, if std dev = 12.4, variance = 12.4^2 = 153.76.
How do you find expectation and variance of a variable using moment generating functions?
The derivative of the moment generating function is the expectation. The variance is the second derivative of the moment generation, E(x^2), minus the expectation squared, (E(x))^2. ie var(x)=E(x^2)-(E(x))^2 :)
Is sigma square equal to variance?
Yes, sigma squared (σ²) represents the variance of a population in statistics. Variance measures the dispersion of a set of values around their mean, and it is calculated as the average of the squared differences from the mean. In summary, σ² is simply the symbol used to denote variance in statistical formulas.
Is the variance of a group of scores the same as the sum of the squared deviations or the average of the squared deviations?
Given a set of n scores, the variance is sum of the squared deviation divided by n or n-1. We divide by n for the population and n-1 for the sample.
1 The average of the squared deviation scores from a distribution mean?
Variance
Symbol for population variance?
the small greek letter sigma squared.
Suppose the standard deviation is 13.1 what is the variance?
13.1 squared = 3.62
What word means the average of the squared deviation scores from a distribution mean?
Variance
