Your book probably has some theorems that cover finding the variance of a sum of multiple of random variables, such as the following.ParisSpart said:The random variable X1, X2,...,X15 are independent and take each values +1,-1 with probability 1/2.
We define Y = sum from j=1 to 15(j*Xj)
whats is the variance VAR(Y)=?
i will find this with VAR(Y)=E(X^2)-(E(X)^2) but how i can find them?
The formula for calculating variance of Y with X1, X2,...,X15 is:
Var(Y) = (1/n) * ∑(Yi - Ȳ)2
where n is the number of observations and Ȳ is the mean of the Y values.
The variance of Y with X1, X2,...,X15 measures the spread or variability of the Y values around their mean. A larger variance indicates a wider range of values, while a smaller variance indicates a more concentrated set of values.
Yes, the variance of Y with X1, X2,...,X15 can be used to compare the spread of Y values between different sets of data. However, it is important to note that the units of measurement for Y must be the same in order for a meaningful comparison to be made.
The variance of Y with X1, X2,...,X15 is directly affected by the number of observations. As the number of observations increases, the variance tends to decrease, indicating a more precise estimate of the variability of Y values.
Variance and standard deviation are both measures of variability. The standard deviation is simply the square root of the variance. This means that the standard deviation is expressed in the same units as the original data, making it easier to interpret.