Answer:
Total Interest Diane has to pay is $1,745
Step-by-step explanation:
<u>Behind the Excel sheet</u>
Total Number of Days:
It was the sum 2016 + 2017 + 3 months of 2018
19 + 365 + 31 + 28 + 4
<u>Exact Intrest on Loan</u>
the Borrowed Amount is multiplied by Exact Intrest Rate multiplied by Total Number of Days divided by Number of Days in a Year
$30,000 x 0.0475 x (447/365)
Answer:
Step-by-step explanation:
Recall that since X is uniformly distributed over the set [1,4] we have that the pdf of X is given by if
and 0 otherwise. In the same manner, the pdf of Y is given by
if
and 0 otherwise.
Note that if Y is in the interval (4,5] then Y>X by default. So, in this case we have that P(Y>X| y in (4,5]) = 1. We want to calculate the probability of having Y in that interval . That is
. Thus,
.
We want to proceed as follows. Using the total probability theorem, given two events A, B we have that
In this case, A is the event that Y>X and B is the event that Y is in the interval (4,5].
If we assume that X and Y are independent, then we have that the joint pdf of X,Y is given by when
. We can draw the region were Y>X and the function h(x,y) is different from 0. (The drawing is attached). This region is described as follows:
and
, then (the specifics of the calculations of the integrals are ommitted)
Thus,
