Variance Ratio Calculation
The variance ratio, often denoted by 'F', is used to compare the variances of two samples or populations. In statistical practice, it is typically calculated by dividing the larger variance by the smaller variance.
We are given:
- Variance of the first yarn: $V_1$
- Variance of the second yarn: $V_2$
- The condition: $V_1 < V_2$
The formula for the variance ratio 'F' is:
$ F = \frac{\text{Larger Variance}}{\text{Smaller Variance}} $Based on the given condition $V_1 < V_2$, we know that $V_2$ is the larger variance and $V_1$ is the smaller variance.
Substituting these into the formula:
$ F = \frac{V_2}{V_1} $Thus, the variance ratio 'F' is $\frac{V_2}{V_1}$.
Important Questions from Variance
- Consider a random variable $X$ with mean $\mu_X = 0.1$ and variance $\sigma_X^2 = 0.2$. A new random variable $Y = 2X + 1$ is defined. The variance of the random variable $Y$ (rounded off to one decimal place) is ________________.
- Variance of the sum of two statistically independent random variables $X$ and $Y$, $\sigma_{X+Y}^2$, is
A continuous random variable $x$ has a probability density function given by
$f(x) = e^{-a|x|} \text{ } (-\infty < x < \infty)$
where $a$ is a real constant. The variance of $x$ is __________ (correct up to one decimal place).
People were prohibited ________ their vehicles near the entrance of the main administrative building.
- Analysis of variance (ANOVA) can be used to compare multiple groups of samples. Select the correct option that reflects the principle behind ANOVA.
