12.4.1

Section 12.4.1 Blog Entry:

Having read section 12.4.1 in the text:

Difficult:
I don't understand why in the second example on page 819 in section 12.4.1 Discrete Distributions, it states that X: Omega (Sample Space) --> R takes on values 1, 2, or 3. Did the text just set R as these random values or is there a reason that these three numbers were chosen? Why is it that Y(H)=1, Y(TH)=2, and Y(TTH)=3? I understand the first example for X(HHH)=3 or X(TTH)=1 or X(TTT)=0, since the number signified the number of heads (H) appeared in the coin tosses, but I do not understand the relationship in the second example.

For the definition of a probability mass function, I was wondering if there was an upper bound for the second condition on page 820. The second condition of the definition is the summation of p(x) from x is equal to 1, where the sum is over all values of X with P(X=x) is greater than 0. Is there an upper bound for this summation of p(x)?

I was wondering where the text derived the statement or assumption on the bottom of page 820 in the "solution" section. The text states that "The function F(x) is defined for all values of x included in R. For instance, F(-2.3) =P(X less than or equal to -2.3)=P(empty set)=0 or F(1)=P(X less than or equal to 1)= P(X= -1 or 0) =0.3. I cannot seem to find a reason for the text to make the statement/assumption that F(-2.3)=P(empty set)=0. Where did they get this from?

Reflective:
I found this section to be rather difficult to comprehend. I did not expect piecewise functions and limit concepts to appear in this section/chapter after all of the probability concepts were covered earlier. I think I still have a difficult time in understanding exactly what the distribution function and probability mass function are for. I think after reading I was able to understand the inner workings and individual steps of how they arrived at some of the numbers using the corresponding values on the charts, but I can't seem to grasp exactly why they would use these methodologies.