2. A student tosses two dice simultaneously. The outcome of the first die is independent of the
outcome of the second die. (a) Write down the sample space, . (b) We are interested in finding out
the probability that the sum of the two die tosses is four or less. Give an appropriate sigma-field.
(c) Suppose both dice are fair. Denote the value on the face of the first and the second die toss as
X and Y, respectively. Define V=X+Y for v=2,3,.,12. We are interested in finding the probability
distribution of V. (i) Construct an appropriate sigma-field where it is meaningful to ask about the
probability distribution of V. (ii) Explain how a probability measure is assigned to an event defined
as "V =11 ". (iii) Find P(V=v)..
This PowerPoint helps students to consider the concept of infinity.
2 A student tosses two dice simultaneously The outcome of .pdf
1. 2. A student tosses two dice simultaneously. The outcome of the first die is independent of the
outcome of the second die. (a) Write down the sample space, . (b) We are interested in finding out
the probability that the sum of the two die tosses is four or less. Give an appropriate sigma-field.
(c) Suppose both dice are fair. Denote the value on the face of the first and the second die toss as
X and Y, respectively. Define V=X+Y for v=2,3,.,12. We are interested in finding the probability
distribution of V. (i) Construct an appropriate sigma-field where it is meaningful to ask about the
probability distribution of V. (ii) Explain how a probability measure is assigned to an event defined
as "V =11 ". (iii) Find P(V=v).
