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torquerotates
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Is this true? In all cases?
The notation "E|X|" refers to the expected value of the absolute value of the random variable X. This is equivalent to the expected value of X when X is a continuous random variable.
The formula for calculating the expected value of a continuous random variable X is: E(X) = ∫xf(x)dx, where f(x) is the probability density function of X. To calculate E|X|, we would replace x with |x| in the formula.
"E|X|=E(X)" tells us that the expected value of the absolute value of X is equal to the expected value of X. This implies that the distribution of X is symmetric around its mean, as the absolute value of a number is always positive.
No, "E|X|=E(X)" is specifically for continuous random variables. For discrete random variables, the notation is typically written as E[|X|] and the formula for calculating it is different.
"E|X|=E(X)" is an important concept in probability theory as it helps us understand the central tendency of a continuous random variable. It tells us the average value of the absolute deviation from the mean, which is useful in analyzing data and making predictions.