helix999 said:I think E[x1]<=E[x2]
helix999 said:but no idea abt std deviation. i don't know if i am correct.
lanedance said:its always a good place to start at the defintions (either discrete or continuous will work)
from the definitions, E[X1]<= E[X2] shoudl be obvious
for the standard deviation, building on clamtrox's argument, it might help to consider the dsicrete variable pdf:
P(X2= x2) = 1, if x2 = b
P(X2= x2) = 0, otherwise
whats the standard deviation of this "random" variable?
statdad said:consider X1 and X2 with distributions
[tex]
\begin{tabular}{l c c c c c}
x & 10 & 20 & 30 & 40 & 50 \\
p(x) & .80 & .1 & .07 & .02 & .01\\
\end{tabular}
Expectation, also known as the mean, is a measure of the central tendency of a dataset. It represents the average value of the data. Standard deviation, on the other hand, is a measure of the spread of the data. It tells us how much the data deviate from the mean.
To calculate the expectation, you add up all the data values and divide by the total number of values. To calculate the standard deviation, you first find the mean, then subtract the mean from each data value, square the differences, add them up, divide by the total number of values, and finally take the square root of the result.
Expectation and standard deviation are important because they help us understand the characteristics of a dataset. The expectation gives us a general idea of the dataset's central value, while the standard deviation tells us how much the data values vary from the mean. These measures are used to make predictions and draw conclusions about a population based on a sample.
Changing the data values can affect the expectation and standard deviation in different ways. If the data values are increased or decreased by a constant value, then the expectation and standard deviation will also increase or decrease by the same value. If the data values are multiplied or divided by a constant, then the expectation will also be multiplied or divided by the same constant, but the standard deviation will be multiplied or divided by the absolute value of the constant.
No, expectation and standard deviation cannot be negative. The expectation represents the average value of the data, so it must be positive or zero. The standard deviation represents the spread of the data, and it cannot be negative because it is calculated by squaring the differences between each data value and the mean. However, it is possible to have a negative standard deviation in certain situations, such as when dealing with financial data or when using a biased estimator for the standard deviation calculation.