Ch 6

Question 1

If Z=(X-E[X])/sqrt(Var(X)) define properties of Z

Answer 1

E[Z]=0 Var(Z)=1 and fZ(x)=sqrt(Var(X))fX(sqrt(Var(X))x+E[X]

Question 2

When does a rv have standard normal distribution?X~N(0,1)

Answer 2

If fX(x)=1/sqrt(2pi)e^(-x^2/2)

Question 3

When does an rv have Gaussian distribution or is normally distributed? X~N(mew,sigma^2)

Answer 3

fX(x)=1/sqrt(2pisigma^2)e^(-(z-mew)^2/2sigma^2)

Question 4

What is distribution of Z=aX+b if X~N(mew, sigma^2)

Answer 4

Z~N(amew +b,a^2sigma^2)

Question 5

What does cdf of standard normal distribution equal when phi(-x)

Answer 5

Phi(-x)=1-Phi(x)

Question 6

What is CLT?

Answer 6

Refer to notes( too long to type)

Question 7

What is CLT in simple terms?

Answer 7

For large n (Xn-E[Xn])/sqrt(Var(Xn) approx ~N(0,1)