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Amount spent for food = $5850, housing = $4680, clothing = $2340, savings = $2600, taxes = $5850, expenses = $2080.
<u>Step-by-step explanation:</u>
Step 1:
Given details are Total Income = $23,400
Step 2:
Amount spent for food, F= 1/4th of 23,400 =
= $5850
Step 3:
Amount spent for housing, H = 1/5th of 23,400 =
= $4680
Step 4:
Amount spent for clothing, C = 1/10th of 23,400 = = $2340
Step 5:
Amount spent for savings, S = 1/9th of 13,400 = = $2600
Step 6:
Amount spent for taxes, T = 1/4th of 23,400 = =$5850
Step 7:
Find amount spent on other expenses by totaling all expenditures and subtracting from the annual income.
Annual Income = F + H + C + S + T + E
Amount spent on other expenses, E = 23400 - (5850 + 4680 + 2340 + 2600 + 5850)
E = 23400 - 21320
E = $2080
a.
is a proper joint density function if, over its support, is non-negative and the integral of
is 1. The first condition is easily met as long as
. To meet the second condition, we require
b. Find the marginal joint density of and
by integrating the joint density with respect to
:
Then
c. This probability can be found by simply integrating the joint density: