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Cara Wales English 4 cards

Cards in this deck (4)

1Chapter 7 - Univariate Continuous Random Variables The probability density function (PDF) of X is a function fx(x) such that Fx(b)=? Equivalently F'x(b)=? If X is continuous and g(.) is a real valued function then E[g(X)]=? The 2 special cases as discussed for discrete random variables also apply here. What are they?Fx(b) = Pr(X
2If X is continuous and g(.) is a real valued function then E[g(X)]=? The 2 special cases as discussed for discrete random variables also apply here. What are they?integral [from -infinity to infinity] g(x)fx(x) dx
1. If g(X) = X then E(X) = integral [from - infinity to infinity] of xfx(x) dx is the mean of x
2. If g(X)= (X-E(X))^2 then E[(X-(E(X))^2] = integral [from -infinity to infinity] (x-E(X))^2fx(x) dx is the variance of X
3Chapter 7 - Expectation E(aX+b)=? Var(aX+b)=? If X and Y are continuous random variables E(X+Y)=? IF X and Y are independent continuous random variables Var(X+Y)=? If Xi, i=1,...,n are independent continuous random variables then: E[SIGMAaiXi]=? Var[SIGMAaiXi]=?aE(X)+b
a^2Var(X)
E(X)+E(Y)
Var(X)+Var(Y)
SIGMAaiE(Xi)
SIGMAai^2Var(Xi)
4Chapter 7 - Moment Generating Function For a continuous random variable X, the moment generating function (MGF) is? We can use the MGF, Mx(t) to calculate the moments of X. How is this done? Mx(0)=? Prove E(X^n)Mx(t) = E[e^tX] = integral [from -infinity to infinity] e^(tx)fx(x) dx
d^n/dt^n{Mx(t)} ¦at the limit t=0 = Mx^(n)(0) = E(X^n)
E(1) = 1
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