Prove Cantor’s original result: for any nonempty set (whether
finite or infinite), the cardinality of S...
Prove Cantor’s original result: for any nonempty set (whether
finite or infinite), the cardinality of S is strictly less than
that of its power set 2S . First show that there is a one-to-one
(but not necessarily onto) map g from S to its power set. Next
assume that there is a one-to-one and onto function f and show that
this assumption leads to a contradiction by defining a new subset
of S that cannot possibly be the image of...
A consequence of continuous random variables having an infinite,
uncountable set of possible values is that...
A consequence of continuous random variables having an infinite,
uncountable set of possible values is that the probability of any
continuous random variable that equals to a specific value is
always ______________.
Multiple Choice
zero
very hard to tell
an extremely small number
less than one
Let S denote the set of all possible finite binary strings, i.e.
strings of finite length...
Let S denote the set of all possible finite binary strings, i.e.
strings of finite length made up of only 0s and 1s, and no other
characters. E.g., 010100100001 is a finite binary string but
100ff101 is not because it contains characters other than 0, 1.
a. Give an informal proof arguing why this set should be
countable. Even though the language of your proof can be informal,
it must clearly explain the reasons why you think the set should...
A Bernoulli trial is an experiment with the sample space
S = {success, failure}. Let X...
A Bernoulli trial is an experiment with the sample space
S = {success, failure}. Let X be the random variable on S
defined by
? X(s) : 1 if s = success
0 if s = failure.
Suppose the probability P ({success}) is equal to some value p ∈
(0, 1).
(a) Tabulate for the rv X the probability distribution
Px (X = x) in terms of p for x ∈ {0, 1}.
(b) Give the expression for the cdf...
we have sample space (S,P) where S is the power set of {1,2} and
P(a) =...
we have sample space (S,P) where S is the power set of {1,2} and
P(a) = |a| / |S| for all a in S (thus |S|=4). We define two random
variables such that for all a in S we have X(a) = |a| and Y(a) = 1
if b is in a and 0 otherwise.
What is the probability that Y(a)=1?
what is the expected value of Y?
What is the variance of Y?
what is the value of P(X=1...
Random variables are used to model situations in which the
outcome, before the fact, is uncertain....
Random variables are used to model situations in which the
outcome, before the fact, is uncertain. One component in the model
is the sample space. The sample space is the list of all possible
outcomes (or a range of possible values). For each value in the
sample space, there is an associated probability. The probability
can either be an estimate of something that exists in the real
world or it could be an exact value that comes from an ideal...
Let the S = {0,1,2,3,4,5,6,7,8,9,10} be the sample space of a
random experiment. Suppose A is...
Let the S = {0,1,2,3,4,5,6,7,8,9,10} be the sample space of a
random experiment. Suppose A is the event that we observe a number
less than 3 and B be the event that we observe a number greater
than 8. Determine the event that either A occurs or B occurs.
Group of answer choices
{3,4,5,6,7,8}
{0,1,2,3,8,9,10}
empty set
{0,1,2,9,10}
{4,5,6,7}
Same Topic:
1. For a finite, equiprobable sample space S, show that
P(A|B) = |A ∩...
Same Topic:
1. For a finite, equiprobable sample space S, show that
P(A|B) = |A ∩ B| |B| , for any two events A, B.
2. Use the result in problem 2 to find P(A|B) where |A| = 25, |A
− B| = 15, and |B − A| = 10.
Note the use of the result from 2 allows us to compute this
conditional probability without actually knowing the size of our
sample space.