School Of Post Graduate Studies
... Unless the data set is rather large, the mode may not be very meaningful. For example, consider the earning per share measurements for the thirty financial companies we used in the previous chapter. If you were to re-examine these data, you would find that none of the thirty measurements is duplicat ...
... Unless the data set is rather large, the mode may not be very meaningful. For example, consider the earning per share measurements for the thirty financial companies we used in the previous chapter. If you were to re-examine these data, you would find that none of the thirty measurements is duplicat ...
Set Theory Digression
... Example: Consider tossing two dice. Let A denote the event of an odd total, B the event of an ace on the …rst die, and C the event of a total of seven. We ask the following: (i) Are A and B independent? (ii) Are A and C independent? (iii) Are B and C independent? (i) P [AjB] = 1=2, P [A] = 1=2 hence ...
... Example: Consider tossing two dice. Let A denote the event of an odd total, B the event of an ace on the …rst die, and C the event of a total of seven. We ask the following: (i) Are A and B independent? (ii) Are A and C independent? (iii) Are B and C independent? (i) P [AjB] = 1=2, P [A] = 1=2 hence ...
Lecture 12 Uniform Integrability
... Xn = 0}. By convention, inf ∅ = +∞. It is well known that a simple symmetric random walk hits any level eventually, with probability 1 (we will prove this rigorously later), so P[ T < ∞] = 1, and, since Yn = 0, for n ≥ T, we have Yn → 0, a.s., as n → ∞. On the other hand, {Yn }n∈N0 is a martingale, ...
... Xn = 0}. By convention, inf ∅ = +∞. It is well known that a simple symmetric random walk hits any level eventually, with probability 1 (we will prove this rigorously later), so P[ T < ∞] = 1, and, since Yn = 0, for n ≥ T, we have Yn → 0, a.s., as n → ∞. On the other hand, {Yn }n∈N0 is a martingale, ...
Chapter 4
... suggests addition. Add P(A) and P(B), being careful to add in such a way that every outcome is counted only once. In the multiplication rule, the word “and” in P(A and B) suggests multiplication. Multiply P(A) and P(B), but be sure that the probability of event B takes into account the previous oc ...
... suggests addition. Add P(A) and P(B), being careful to add in such a way that every outcome is counted only once. In the multiplication rule, the word “and” in P(A and B) suggests multiplication. Multiply P(A) and P(B), but be sure that the probability of event B takes into account the previous oc ...
Chapter 4
... suggests addition. Add P(A) and P(B), being careful to add in such a way that every outcome is counted only once. In the multiplication rule, the word “and” in P(A and B) suggests multiplication. Multiply P(A) and P(B), but be sure that the probability of event B takes into account the previous oc ...
... suggests addition. Add P(A) and P(B), being careful to add in such a way that every outcome is counted only once. In the multiplication rule, the word “and” in P(A and B) suggests multiplication. Multiply P(A) and P(B), but be sure that the probability of event B takes into account the previous oc ...
