At Rick's Pizza, they always put exactly 6 pieces of pepperoni on each slice of pizza. Each pizza has 10 slices. How many pieces
2 answers:
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Answer:
Step-by-step explanation:
Given that X has the following pdf.
x -1 0 2 6 7 Total
P(X) 0.3 0.1 0.3 0.2 0.1 1
xP(X) -0.3 0 0.6 1.2 0.7 2.2
x^2P(X) 0.3 0 1.2 7.2 4.9 13.6
Var(x) 13.6-2.2^2 8.76
Std dev 2.959729717
5)
6. Find the cumulative distribution function F(x) and calculate F(3.2) =
x -1 0 2 6 7
P(X) 0.3 0.1 0.3 0.2 0.1
F(x) 0.3 0.4 0.7 0.9 1
F(3.2) = P(X<3.2) = ___F(X<6) = 0.7__________
7. E(X) = ______2.2_____
8. Var(X) = ____8.76______
Answer:
Step-by-step explanation:
As the statement is ‘‘if and only if’’ we need to prove two implications
is surjective implies there exists a function
such that
.
- If there exists a function
Let us start by the first implication.
Our hypothesis is that the function is surjective. From this we know that for every
there exist, at least, one
such that
.
Now, define the sets . Notice that the set
is the pre-image of the element
. Also, from the fact that
is a function we deduce that
, and because
the sets
are no empty.
From each set choose only one element
, and notice that
.
So, we can define the function as
. It is no difficult to conclude that
. With this we have that
, and the prove is complete.
Now, let us prove the second implication.
We have that there exists a function such that
.
Take an element , then
. Now, write
and notice that
. Also, with this we have that
.
So, for every element we have found that an element
(recall that
) such that
, which is equivalent to the fact that
is surjective. Therefore, the prove is complete.