Three people, X, Y, Z, in order roll an ordinary die. The first
one to roll...
Three people, X, Y, Z, in order roll an ordinary die. The first
one to roll an even number wins. The game continues until someone
rolls an even number. Determine the probability that either Y or Z
will win.
1) If x, y, z are consecutive integers in order then 9 | (x+y+z)
⟺ 3 | y. (Do proof)
2) Let x, y be consecutive even integers then (x+y) is not
divisible by 4. (Show proof and state why it was used)
Let z=e^(x) tan y.
a. Compute the first-order partial derivatives of z.
b. Compute the second-order partial derivatives of z.
c.∗ Convert z = f(x,y) into polar coordinates and then compute
the first- order partial derivatives fr and fθ by directly
differentiating the com- posite function, and then using the Chain
Rule.
The newest invention is a three-sided die. On any roll of this
die, the result is 1 with probability 1/2, 2 with probability 1/4,
and 3 with probability 1/4.
Consider a sequence of six independent rolls of this die.
A. Find the probability that exactly two of the rolls result in
a 3.
B. Given that exactly two of the six rolls resulted in a 1, find
the probability that the first roll resulted in a 1.
C. We are...
The curried version of let f (x,y,z) = (x,(y,z)) is
let f (x,(y,z)) = (x,(y,z))
Just f (because f is already curried)
let f x y z = (x,(y,z))
let f x y z = x (y z)
Peter rolls an 8 die and then Kate gets three chances to roll a
6-die and get greater number than whatever Pter rolled. What is the
probability that at least one of Kate’s rolls is greater than what
Peter's rolls?
Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}.
a) Prove or disprove: A ⊆ X
b) Prove or disprove: X ⊆ A
c) Prove or disprove: P(X ∪ Y ) ⊆ P(X) ∪ P(Y ) ∪ P(X ∩ Y )
d) Prove or disprove: P(X) ∪ P(Y ) ∪ P(X ∩ Y ) ⊆ P(X ∪ Y )