1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
marta [7]
3 years ago
9

Let X denote the temperature (degree C) and let Y denote thetime in minutes that it takes for the diesel engine on anautomobile

to get ready to start. Assume that the joint density for(X,Y) is given by fxy (x,y) = c(4x + 2y +1) ; 0 < x< 40 and 0 < y <2.
(a) Find the value of c that makes this a density.
(b) Find the probability that on a randomly selected day theair temperature will exceed 20 degrees C and it will take at least1 minute for the car to be ready to start.
(c) Find the marginal densities for X and Y.
(d) Find the probability that on a randomly selected day itwill take at least one minute for the car to be ready tostart.
(e) Find the probability that on a randomly selected day theair temperature will exceed 20 degrees C.
(f) Are X and Y independent? Explain on mathematicallybasis.
Mathematics
1 answer:
BlackZzzverrR [31]3 years ago
4 0

Answer:

Step-by-step explanation:

Given f_{XY} (x,y) = c(4x + 2y +1) ; 0 < x < 40\,and\, 0 < y

a)

we know that \int\limits^\infty_{-\infty}\int\limits^\infty_{-\infty} {f(x,y)} \, dxdy=1

therefore \int\limits^{40}_{-0}\int\limits^2_{0} {c(4x+2y+1)} \, dxdy=1

on integrating we get

c=(1/6640)

b)

P(X>20, Y>=1)=\int\limits^{40}_{20}\int\limits^2_{1} {\frca{1}{6640}(4x+2y+1)} \, dxdy

on doing the integration we get

                        =0.37349

c)

marginal density of X is

f(x)=\int\limits^2_{0} {\frca{1}{6640}(4x+2y+1)} \, dy

on doing integration we get

f(x)=(4x+3)/3320 ; 0<x<40

marginal density of Y is

f(y)=\int\limits^{40}_{0} {\frca{1}{6640}(4x+2y+1)} \, dx

on doing integration we get

f(y)=\frac{(y+40.5)}{83}

d)

P(01)=\int\limits^{40}_{0}\int\limits^2_{1} {\frca{1}{6640}(4x+2y+1)} \, dxdy

solve the above integration we get the answer

e)

P(X>20, 0

solve the above integration we get the answer

f)

Two variables are said to be independent if there jointprobability density function is equal to the product of theirmarginal density functions.

we know f(x,y)

In the (c) bit we got f(x) and f(y)

f(x,y)cramster-equation-2006112927536330036287f(x).f(y)

therefore X and Y are not independent

You might be interested in
Joan had 198 dollars to spend on 9 books.After buying them she had 18 dollars. How much did each book cost?
Fed [463]
She spent 20 dollars on each book because if you subtract 18 from 198 you'll get 180 then you divide that by 9 n it leaves you with 20.
3 0
3 years ago
Simplify 5 1/3•5 2/3
Nadusha1986 [10]

Answer:

17 7/9 or 17.7

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
What is this expression in simplest form?
gayaneshka [121]

Answer:

A. 1÷(X+1) (x-2)

some steps are directly

tag me in brainlist if you like it

8 0
2 years ago
The diameter of a circle on
Rama09 [41]
I’m pretty sure it’s c
6 0
3 years ago
1. Write an expression using symbols:
ycow [4]

Answer:

the sum of x and y=x+y

the product of 5 And y minus x is 5(y)-x

the difference between p and q is p-q

the sum of m and n divided by 3 is (m+n)÷3

6 0
2 years ago
Other questions:
  • What is the answer ?
    15·2 answers
  • AB, CD, and EF are straight lines intersecting at point O. Find x.
    9·1 answer
  • Solve the inequality x + 3 &lt; 7. Which number line represents the solution?<br> es )
    10·1 answer
  • I need help with my homework
    9·1 answer
  • A smartphone costs $250. Sale tax is 6%. What is the total cost, including tax?
    11·1 answer
  • What is 5x – 8x + 2 + 5=
    13·2 answers
  • The Hawks are starting a babysitting business. They charge an initial deposit of $25 and a rate of $4 an hour. A linear model is
    6·1 answer
  • How long would it take for your investment to double if it is compounded continuously at 8.5% interest rate?​
    13·1 answer
  • Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.
    7·1 answer
  • Find possible zeroes<br> f(x)=3x^6+4x^3-2x^2+4
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!