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
Ray Of Light [21]
3 years ago
7

A system has one each of two different types of components in joint operation. Let X and Y denote the random lengths of the live

s, in hundreds of hours, for components of type I and type II, respectively. The joint density function is:________

Mathematics
1 answer:
RSB [31]3 years ago
3 0

Answer:

The value of E(Y/X) is 2.

Step-by-step explanation:

As the complete question is not given, thus the complete question is found online and is attached herewith.

So the joint density function is given as

f(x,y)=\left \{ {{\dfrac{x}{8}e^{-\dfrac{x+y}{2}}    \,\,\,\,0 \leq x,0\leq y \atop {0}} \right.

So the marginal function for X is given as

f_x=\int\limits^{\infty}_0 {f(x,y)} \, dy\\f_x=\int\limits^{\infty}_0 \dfrac{x}{8}e^{-\frac{x+y}{2} }dy\\f_x=\int\limits^{\infty}_0 \dfrac{x}{8}e^{-\frac{x}{2}}e^{-\frac{y}{2} }dy\\f_x= \dfrac{x}{8}e^{-\frac{x}{2}}\int\limits^{\infty}_0e^{-\frac{y}{2} }dy\\f_x= \dfrac{x}{4}e^{-\frac{x}{2}}

Now

f(Y/X)=\dfrac{f(X,Y)}{f(X)}\\f(Y/X)=\dfrac{\dfrac{x}{8}e^{-\frac{x+y}{2} }}{\dfrac{x}{4}e^{-\frac{x}{2}}}\\f(Y/X)=\dfrac{1}{2}e^{-\frac{y}{2} }

Now the value of E(Y/X) is given as

E(Y/X)=\int\limits^{\infty}_0 {yf_{Y/X}} \, dy \\E(Y/X)=\int\limits^{\infty}_0 {y\dfrac{1}{2}e^{-\frac{y}{2} } }\, dy\\E(Y/X)=\dfrac{1}{2}\dfrac{\sqrt{2}}{(\dfrac{1}{2})^2}=2

So the value of E(Y/X) is 2.

You might be interested in
Need help ace<br><br> help pls
Alexandra [31]

Answer:

Hello I am an ace! answer: 8

Step-by-step explanation:

Volume for a cube is just length × width × height so you only need to know 1 for a cube because they will all be the same number so 8 is the answer because 8 × 8 × 8 = 512 Hope this helps!

8 0
2 years ago
One day, 148 copies of the student
Romashka-Z-Leto [24]

Answer:

312 copies

Step-by-step explanation:

100 + 100 = 200

40 + 60 = 100

8 + 4 = 12

200 + 100 + 12 = 312 copies

6 0
2 years ago
Read 2 more answers
Find the area of the trapezoid.<br> Answer options: 8sqrt2, 4sqrt3, 12.0, 16sqrt2
Elis [28]

Answer:

=  8sqrt2

Step-by-step explanation:

Area of a trapezium is given by the formula;

1/2(a+b)h ;

Where a and b are the parallel sides and h is the perpendicular height.

a = 3 cm, b= 5 cm

To get; h, we use the Pythagoras theorem;

h² = 3² - 1²

   h² = 8

h = √8

  = √4√2

 = 2√2

Thus;

Area = 1/2(3 +5) 2√2

         = 1/2 ×8 × 2√2

       <u>  = 8√2 cm² or  8sqrt2 cm²</u>

8 0
3 years ago
Which of these is an example of a literal equation? A. 3x – 4y B. 12 = 9 + 3x C. 6 + 30 = 62 D. ax – by = k
nika2105 [10]
I think the answer is D.
8 0
3 years ago
Read 2 more answers
Graph the linear equation. Find three
Karo-lina-s [1.5K]
-3y = -2x -6

Y= 2/3x + 2


When x= 3
Y= 2/3(3) + 2
Y= 2+2 = 4

(3,4)


When x= 6
Y=2/3(6)+2
Y= 4+2 = 6

(6,6)


When x= 12
Y= 2/3(12) + 2
Y= 8+2=10

(12,10)
4 0
3 years ago
Read 2 more answers
Other questions:
  • If a scatter plot has a positive correlation, that would be the same as if a graph has a negative slope.
    10·1 answer
  • Solve the equations below for x. Please show your math work step by step.
    15·1 answer
  • Two sides of a triangle measure 9 cm and 23 cm what could be the measurement of the third side of the triangle
    9·1 answer
  • Suppose a mouse is placed in the maze at the right. If each direction
    13·1 answer
  • What is the sum of the first nine terms of this Sequence if the first term is 0?
    12·2 answers
  • Solve the equation 2/3y - 2/5=5
    6·1 answer
  • 35 + (15) + (-7) + 10
    11·2 answers
  • The half life of a medication is the amount of time for half of the drug to be eliminated from the body. The half life of advil
    10·1 answer
  • What is the area of the circle?
    14·1 answer
  • Miguel deposits $5000 in an account
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!