Question

in an experiment , two dice are tossed , all outcomes are equally likely . Let X the RV such that X is the product of the two numbers of the dots shown .

a) Find the sample space of X.

b) Find pmf of X .

Answer #1

1. A random experiment consists of throwing a pair of dice, say
a red die and a green die, simultaneously. They are standard
6-sided dice with one to six dots on different faces. Describe the
sample space.
2. For the same experiment, let E be the event that the sum of
the numbers of spots on the two dice is an odd number. Write E as a
subset of the sample space, i.e., list the outcomes in E.
3. List...

Let Y denote the number of “sixes” that occur when two dice are
tossed. (Each of these dice has six sides with one, two, three,
four, five, and six dots respectively. Note that the random
variable is not the number of dots).
(a) When two dice are tossed, how many outcomes are possible?
Write out these outcomes. (Hint: your outcomes should correspond to
the number of 6s since that is the random variable here.)
(b) Derive the probability distribution of...

An experiment consists of rolling two fair dice and adding the
dots on the two sides facing up. Using the sample space provided
below and assuming each simple event is as likely as any other,
find the probability that the sum of the dots is 9.

An experiment consists of rolling two fair dice and adding the
dots on the two sides facing up. Using the sample space provided
below and assuming each simple event is as likely as any other,
find the probability that the sum of the dots is 4 or 9.

Suppose that a sample space consists of ? equally likely
outcomes.
Select all of the statements that must be true.
a. Probabilities can be assigned to outcomes in any manner as
long as the sum of probabilities of all outcomes in the sample
space is 1.
b. The probability of any one outcome occurring is 1?.1n.
c. Any two events in the sample space have equal probablity of
occurring.
d. The probability of any event occurring is the number of...

Two regular 6-sided dice are tossed. (See the figure below for
the sample space of this experiment.)
Determine the number of elements in the sample space for tossing
two regular 6-sided dice.
n(S) =
Let E be the event that the sum of the pips on the
upward faces of the two dice is 6. Determine the number of elements
in event E.
n(E) =
Find the probability of event E. (Enter your
probability as a fraction.)

1. Two dice are tossed in a row. Let X be the outcome of the
first die, and let Y be the outcome of the second die. Let A be the
event that X + Y ≤ 7, and let B be the event that X − Y ≥ 2.
(a) Find P(A).
(b) Find P(B).
(c) Find P(A ∩ B).
(d) Are A and B independent?

Two dice are tossed and the absolute value of the difference of
the numbers showing is recorded. Find the expected value of this
experiment.

Two dice are rolled. Let X be the maximum number obtained.
(Thus, if 1 and 2 are rolled, X = 2; if 5 and 5 are rolled, X = 5.)
Assume that all 36 elements of the sample space are equally likely.
Find the probability function for X. That is, find P(X = x), for x
= 1, 2, 3, 4, 5, 6.

In a given experiment, there are four equally likely outcomes
ξ1, ξ2, ξ3, ξ4 and two events A = {ξ1, ξ2} and B = {ξ2, ξ3}.
Compute P [ABc], P [BAc], P [AB], P [A ∪ B].

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