Homework Statement
A trial consists of tossing two dice. The result is counted as successful if the sum of the
outcomes is 12. What is the probability that the number of successes in 36 such trials is
greater than one? What is this probability if we approximate its value using the Poisson...
Homework Statement
Discrete random variables X and Y , whose values are positive integers, have the joint probability mass function , (, ) = 2−−. Determine the marginal probability mass functions () and (). Are X and Y independent? Determine [], [ ], and [ ].
The Attempt at a Solution...
Homework Statement
The old TV game Let’s Make a Deal hosted by Monty Hall could be summarized as
follows. Suppose you are on a game show, and you are given the choice of three doors.
Behind one door is a car, behind the others, goats. You pick a door, say number 1,
and the host, who knows...
Homework Statement
Suppose that the integer values 1 2 and 3 are written on each of three different cards. Suppose you do not know which number is the lowest (you do not know beforehand what the values on the cards are). Suppose that you are to be offered these cards in a random order. When...
Homework Statement
Consider a team of 11 soccer players, all of whom are equally good players
and can play any position.
(a) Suppose that the team has just finished regulation time for a play-off game and
the score is tied with the other team. The coach has to select five players for...
Homework Statement
use induction to prove
(my formatting is off sorry)
\overline{n} \sum \underline{k=1} f _{2k-1} = f_{2n}
The Attempt at a Solution
To start we need to show that f3 is valid. So we show that f2 + f1 = f3, which is the case.
The next part is the confusing part for me. Do...
Homework Statement
using set theroetic notation, write down and prove the contra-positive of:
GOD WHAT IS WRONG WITH LATEX??? It is completely ruining my set notation! And i can't fix it!
If B \cap C \subseteq A Then (C-A) u (B-A) is empty.
The Attempt at a Solution
I'm awful with set...
Homework Statement
state whether the equivalences are valid for P and Q
(latex is screwing up, wherever a letter has been made into superscript it should be normal and there should be a ^ in front of it).
1.. poop \exists x [ P(x) ^ \wedge p Q(x) ] \equiv \exists x P(x) \wedge \exists x Q(x)...
I am having much trouble with indefinite integrals - i get most of the basic theory behind them but as soon as i am confronted with a larger more complex question i get stuck too easily.
These questions are not for my homework, they are just practice for my test. Any hints, tips and general...
Homework Statement
let A be any set of numbers and let R and S be relations on A.
if S and R are symmetric then show S o R is symmetric.
if S and R are antisymmetric then show S o R is antisymmetric.
if S and R are transitive then show S o R is transitive.
if S and R are...
Homework Statement
Let A = { 2,3,5,10,15 } and R be {(2,10),(5,10),(3,15),(5,15)}
find the smallest equivalence on A containing R
find the smallest total order on A containing R
The Attempt at a Solution
so firstly i must show that my new relation containing R is reflexive...
Homework Statement
For each of the relations on the set R x R - (0,0) (ie. no origin) :
- prove it is an equivalence
- give the # of equivalence cases
- give a geometric interpretation of the equivalence cases assuming an element of R x R is a point on a plane
a) {((a,b),(c,d)) |...
Homework Statement
give an inductive proof for all n >= 1
(2a+b) + (4a+b) + ... + (2na + b) = n(an + a + b)
The Attempt at a Solution
In order to start the method of inductoin i have to prove that f(1) holds true.
I am confused by the ... in this equation though.
If n = 1...
Homework Statement
Show that there does not exist integers x,y,z such that
2x + 4y === 1 (mod 7)
x + y + 4z === 2 (mod 7)
y + 3z === 3 (mod 7)
The Attempt at a Solution
Should i be using substitution or elimination to solve this?
I could do something like
2x + 4y + 0z
x...
Homework Statement
let a and b be relatively prime positive integers.
if c is a positive integer and a | bc then prove that a | c
The Attempt at a Solution
I started by trying to prove the contra-positive. If a is not divisible by bc then a is not divisible by c.
it follows that a mod bc...
Homework Statement
for sets A, B and S with S being a subset of B, and a function f: A --> B we define:
f^{-1}(S) = { a \in A : f(a) \in S }
find f^{-1}(S) for:
1) f(x) = x - floor(x) where S = { y: 0 < y < 1 }
2) f(x) = x^{3}-7x+16 where S = { y: 10 <= y <= 22 }
3) f(t) = (cos(t),sin(t))...
Homework Statement
Let a,b,c E R with b != ac and let the function f : R --> R be given by
f(x) = a if x = c
f(x) = (ax - b) / (x - c) if x != c
Show that f(x) is one-to-one
Show that f(x) is onto
Show the inverse of f(x)
The Attempt at a Solution
I don't want anyone...