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
devlian [24]
3 years ago
6

Show that the following functions are probability density functions for some value of k and determine k. Then, determine the mea

n ((a),(c),(e),(g)) and variance ((b),(d),(f),(h)) of X. Round your answers to three decimal places (e.g. 98.765).
(a),(b)f (x) = kx2 for 0 < x < 23
(c),(d)f (x) = k(1 + 2x) for 0 < x < 20
(e),(f)f (x) = ke-x for 0 < x
(g),(h)f (x) = k where k > 0 and 110 < x < 110 + k


(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Mathematics
1 answer:
lord [1]3 years ago
8 0

Answer:

a) 17.5

b) 15.6

c) 13.3

d) 21.51

Step-by-step explanation:

The given function is equal to:

f(x)=kx^2

where

\int\limits^y_0 {kx^{2} } \, =1

where y=23

Clearing k=0.00025

a) Ex=\int\limits^y_0 {xf(x)} \, dx =\int\limits^y_0 {x*0.00025x^{2} } \, dx =17.5

b)Vx=Ex^{2} -(Ex)^{2} =\int\limits^y_0 {x^{2}f(x) } \, dx-17.5^{2}  =\int\limits^y_0 {x^{2} *0.00025x^{2} } \, dx -17.5^{2} =321.82-306.25=15.6

c) The function is equal to:

f(x)=k(1+2x)

\int\limits^y_0 {k(1+2x)} \, =1

where y=20

k=0.0024

Ex=\int\limits^y_0 {xf(x)} \, dx =\int\limits^y_0 {x*0.0024(1+2x)} \, dx =13.3

d) Vx=Ex^{2} -(Ex)^{2} =\int\limits^y_0 {x^{2} f(x)} \, dx -13.3^{2}=\int\limits^y_0 {x^{2} *0.0024(1+2x)} \, dx-13.3^{2}   =198.4-176.89=21.51

You might be interested in
SOMEBODYY HELP ILL GIVE BRAINLYY......
ANTONII [103]

Step-by-step explanation:

a^2+b^2 = c^2

C is the biggest number, so put in all the numbers in the equation then if it's equal then it's a right triangle.

example: 6^2 + 8^2 = 10^2

36 + 64 = 100

100 = 100

this one is a right angle because the two sides is equal to the hypotenuse(largest number).

3 0
3 years ago
What do I have to do
hichkok12 [17]

Answer:

+15

-721

0

+462

-1200

The positives are because it said 'above sea level', the negatives because it said 'below sea level' and zero because it said 'sea level'.

3 0
3 years ago
Find the volume of the cylinder
yulyashka [42]

Answer:

14130 {ft}^{3}

4 0
3 years ago
Help pls √-4 - √-25<br> Express complex numbers in terms of i
kow [346]

i=\sqrt{-1}\\\\\sqrt{-4}=\sqrt{(4)(-1)}=\sqrt4\cdot\sqrt{-1}=2i\\\\\sqrt{-25}=\sqrt{(25)(-1)}=\sqrt{25}\cdot\sqrt{-1}=5i\\\\\sqrt{-4}-\sqrt{-25}=2i-5i=-3i

5 0
3 years ago
Read 2 more answers
Is the simplified form of 2-3 + 3.3 rational?<br> Yes<br> No
N76 [4]

Answer:

YES IT IS

Step-by-step explanation:

2-3 + 3.3

= -1 + 3.3

= -4.3

We learn that:

Rational number: rational number is the number that can be written as a/b (a and b would be intergers and b is not equal to 0). Rational number would be most of numbers we use in out life, except Square root and Pi number.

In this case, -4.3 can be write as -43/10

So YES it would be a rational number

Hope this helped :3

6 0
3 years ago
Other questions:
  • A large jar contains 1380 coins. The result of 40 coins pulled at random from the jar is given below.
    5·2 answers
  • Find valuable asked for witch ABCD must be a parallelogram, <br> 1<br> 11<br> 2<br> 15
    14·1 answer
  • An experiment consist of rolling 3 fair dice (1 red die, a blue die, and a white die) and recording the number rolled on each di
    12·1 answer
  • Which operation should be performed first according to the order of operations? 75 – 12 + 36 ÷ 3 + 14 • 8 A. 12 + 36 B. 75 – 12
    15·2 answers
  • One of the factors of the polynomial x3 + 5x2 + 6x is (x2 + 3x). What is the other factor?
    10·2 answers
  • Are ZK and 2B corresponding angles? Explain.
    13·2 answers
  • Help me out here pleaseeeeeeee
    11·2 answers
  • What is tan B?<br> А<br> 34<br> 16<br> В<br> 30<br> с<br> 15
    8·1 answer
  • Nancy borrowed $150 from her parents to buy a video game system. She has agreed to pay them back $25 each week Which equation re
    12·1 answer
  • Is the average amount spent on textbooks per semester by accounting majors significantly
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!