C p t t ft t et eln 2t 2t and p t 1t

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: how spread out 2 the distribution of X is. As before, the variance of X is often denoted by σX , where σX = Var(X ) is called the standard deviation of X . If X is a measurement in some units, then σX is in the same units. For example. if X represents a measurement in feet, then Var(X ) represents a number of feet2 and σX represents a number of feet. Exactly as shown in Section 2.2 for discrete-type random variables, the variance for continuous-type random variables scales as Var(aX + b) = a2 Var(X ). −µ The standardized random variable, XσX X , is a dimensionless random variable with mean zero and variance one. Finally, as before, the variance of a random variable is equal to its second moment minus the square of its first moment: Var(X ) = E [X 2 − 2µX X + µ2 ] X = E [X 2 ] − 2µX E [X ] + µ2 X = E [X 2 ] − µ2 . X Example 3.2.2 Suppose X has the following pdf, where A is a constant to be determined: fX (u) = A(1 − u2 ) −1 ≤ u ≤ 1 0 else. Find A, P {0.5 < X < 1.5}, FX , µX , Var(X ), and σX . 76 Solution: CHAPTER 3. CONTINUOUS-TYPE RANDOM VARIABLES To find A we require that ∞ 1...
View Full Document

This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Tech.

Ask a homework question - tutors are online