Chapter 4

Question 1

What is the pdf of a r.v. X with an exponential distribution?

Answer 1

f(x;l) = l * e^-(l*x) when x >= 0, 0 otherwise

Question 2

What is the cdf of a r.v X with an exponential distribution?

Answer 2

F(x;l) = 1 - l * e^-(l*x) when x >= 0, 0 otherwise

Question 3

If X has a normal distribution with mean u and standard deviation sigma what is Z?

Answer 3

Z = (X - u) / sigma

Question 4

What is P(a less= x less=b)

Answer 4

= O((b - u) / sigma) - O((a - u) / sigma)

Question 5

What is P(X less= a)

Answer 5

= O((a - u) / sigma)

Question 6

What is P(X >= a) if X has a normal distribution?

Answer 6

= 1 - O((a - u) / sigma)

Question 7

What is V(X)?

Answer 7

it is variance and it = E(X^2) - [E(X)]^2

Question 8

What is the P(X > t) where X has an exponential distribution?

Answer 8

e^(lambda*t)

Question 9

What is the P( X

Answer 9

1 - P(X > t)

Question 10

P(A|B)

Answer 10

= P( A n B)/ P(B)

Question 11

What is the a formula for standard deviation?

Answer 11

Sqrt((1/n-1)(sum(Xi^2) - (sum(Xi)^2)/n))