An insurance company offers two types of insurance: health insurance and life insurance. Let X be the annual claim on the health insurance and Y be the annual claim on the life insurance. The joint density function of X and Y is: Find the probability that the total claims exceed 0.5 but is less than 2 and the claim on the life insurance is less than 1.5.

The joint density equation is missing in the question. The equation is [tex]f(x,y)=\left\{\begin{matrix}2x^3, 0\leq x\leq 1,0\leq y\leq 2\\ 0, \text{ otherwise}\end{matrix}\right.[/tex]

Probability is 0.59

Step-by-step explanation:

We have

x -- denotes the annual claim health insurance

y -- denotes the annual claim life insurance

And joint density of x and y is given to us

[tex]f(x,y)=\left\{\begin{matrix}2x^3, 0\leq x\leq 1,0\leq y\leq 2\\ 0, \text{ otherwise}\end{matrix}\right.[/tex]

Event that the claim exceeds 0.5 but less than 2 can be written as 0.5≤ x+y ≤2

and claim of life insurance less than 1.5 can be written as 0 ≤ y ≤ 1.5

Required probability

= P( 0.5≤ x+y ≤2  ∩ 0 ≤ y ≤ 1.5 )

Lets plot this, to find the common region

For common region

when 0≤ x ≤ 0.5, then 0.5 ≤ y ≤ 1.5  ---- for region I

when 0.5≤ x ≤ 1, then 0 ≤ y ≤ 2-x  ---- for region II

The required probability

= [tex]\int_{0}^{0.5} \int_{0.5-x}^{1.5}2x^3 dy dx+\int_{0.5}^{1} \int_{0}^{2-x}2x^3 dy dx[/tex]

= [tex]\int_{0}^{0.5} 2x^3[\int_{0.5-x}^{1.5}dy] dx+\int_{0.5}^{1} 2x^3[\int_{0}^{2-x}dy] dx[/tex]

= [tex]\int_{0}^{0.5} 2x^3(1.5-0.5+x) dx+\int_{0.5}^{1} 2x^3 (2-x) dx[/tex]

= [tex]\int_{0}^{0.5}2x^3 dx+\int_{0}^{0.5}2x^4 dx+\int_{0.5}^{1}4x^3 dx-\int_{0.5}^{1}2x^4[/tex]

= [tex][\frac{2x^4}{4}]_0^{0.5}+[\frac{2x^5}{5}]_0^{0.5}+[\frac{4x^4}{4}]_{0.5}^1-[\frac{2x^5}{5}]_{0.5}^1[/tex]

= [tex]$\frac{1}{32}+\frac{1}{80}+\frac{1}{16}-\frac{31}{20}$[/tex]

= 19/32

=0.59    

4 kitchen assistants can prepare 10kg of vegetables in 45 minutes. How long would it take 25 assistants to prepare

State the domain and range in set notation​

If r objects are being selected from a group of n distinct objects and order does matter, then this arrangement is known as a

OPEN ENDED QUESTION
Rewrite the following problem using
commutative property of addition: -3 + 7

Item 3 A snail travels 3/8 feet in 1/2 hour. How many feet does the snail travel in one hour? Express your answer in simplest form. 3/16ft 1/4ft 1/8ft 3/4ft

a gallon of paint can cover about 350 square feet of wall space. You have measured a wall to be 210 inches by 120 inches. Will one gallon of paint be enough to cover the wall?

what is -66 2/3 - 24 1/8 + -78 3/4

If you get this you are a critical thinker. I enter the garden. There are 34 people. You kill 30. How many people are in the garden. Good luck! If you get it correct your answer will be deleted and l will message you to continue the game.
​

Suppose 7 quarters, 4 dimes, 4 nickels, and 3 pennies are in a box. One coin is selected at random. What is the expected value of the money drawn from the box?

The Lions won 35 out of 40 games this season. What fraction of the games did the Lions win?Write your answer in simplest form.___________________________________

A technician compares repair costs for two types of microwave ovens (type I and type II). He believes that the repair cost for type I ovens is greater than the repair cost for type II ovens. A sample of 61 type I ovens has a mean repair cost of $79.60, with a standard deviation of $23.47. A sample of 45 type II ovens has a mean repair cost of $75.25, with a standard deviation of $15.07. Conduct a hypothesis test of the technician's claim at the 0.05 level of significance. Let μ1 be the true mean repair cost for type I ovens and μ2 be the true mean repair cost for type II ovens.Step 3 of 4 : Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to three decimal places.

Can you solve (x-2)(x+3)=5 by solving x-2=5 and x+3=5? Explain

Will MARK BRAINLIEST

12 x 3 x 8 + 3 + 1 - 100 x 2323

two groups of people need to get to the top floor of a building. the first. group had 33 people, and its elevator can carry 6 people per trip. the second group has 49 people,but its elevator can carry 7 people per trip..... group 1 is represented by the equation 6x=33. solving the equation gives x what​

Help. Your backyard is 10 feet longer than it is wide. Its area is 8624 square feet. Its width is Solve in quadratic equation.

Please help!! What is the quotient??

What is the degree of the polynomial

factor an expression:
(x²+x+1)²+3x(x²+x+1)-18x²​

a well is being dug into the ground. the well needs to reach the depth of 120 feet. a machine can dig down in 12 minutes. what is the change in depth each minute the machine is digging​

Is x a natural number

10X10 in exponent form?

work out the difference in minutes between 1 hour 25 minutes and 1 1/4 hours step by step please :)

State the horizontal asymptote of the rational function.
f(x) = quantity x plus nine divided by quantity x squared plus four x plus two

How many days equal 7344 minutes?

study of class attendance and grades among first-year students at a state university showed that, in general, students who missed a higher percent of their classes earned lower grades. Class attendance explained 36% of the variation in grade index among the students. What is the numerical value of the correlation between percent of classes attended and grade index?

PLEASE HELP IF YOU KNOW ​

A line passes through (0, 2) and has a slope of 3. Which function's graph is parallel to this line?
A. f(x) = 2 O
B. f(x) = 3 O
C. f(x) = 2x O
D. f(x) = 3x o TUL earch​

Dante’s cell phone company charges $45 per month for unlimited calls and texts,plus $0.25 per gigabyte of data.His last cell phone bill was $60.50.How many gigabytes of data did Dante use last month?

A scuba driver was swimming at an elevation of -8 meters. A shark was swimming at an elevation of -29 meters. Find the difference between these two elevations.

Find the interest

earned:

$ 15,500 for 7.5 years

at 4.9% annual

compound interest