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
Licemer1 [7]
4 years ago
5

Let X be a random variable with CDF given byFX(t) =0 for t < 1,1 /2 for ?1 t < 11/ 2 t for 1 t < 21 for t 2Calculate E[

X]
Mathematics
1 answer:
nydimaria [60]4 years ago
3 0

Answer:

\mathbf{E(X) = \dfrac{3}{4}}

Step-by-step explanation:

From the given data, the cumulative distribution function of a random variable can be represented as:

F_X(t)  =\left\{ \begin{array}{c}0........... t

The objective is to estimate E(X), to do that, let's first evaluate the probability density function by differentiating the cumulative distribution function from above.

f_X(x) =\left \{ {{\dfrac{1}{2} .......1 \leq x \leq 2 } \atop {0..... otherwise }} \right.

∴

f_X(t)  =\left\{ \begin{array}{c} \dfrac{d}{dx}(0)=0...........

The expected value of x i

.e E(X) can now be estimated by taking the integral:

E(X) =  \int ^{\infty}_{\infty}  x f(x) \ dx

E(X) =  \int ^{1}_{- \infty}  x 0 dx + \int^2_1 \ x \dfrac{1}{2}\ dx + \int ^{\infty}_2 \ x0dx

E(X) =  \int ^{2}_{1}  x \dfrac{1}{2} dx

E(X) = \dfrac{1}{2}[\dfrac{x^2}{2}]^2_1

E(X) = \dfrac{1}{2}[\dfrac{4}{2}-\dfrac{1}{2}]

E(X) = \dfrac{1}{2} \times [\dfrac{3}{2}]

\mathbf{E(X) = \dfrac{3}{4}}

You might be interested in
I need help it's so important if u answer them correctly u will be named the branliest
Mkey [24]
1. No it is not because it is false. It is false because for it to be three times as many wins as jim, jim would need around 166 or less wins to make cy have three times the wins. 2. i believe the graph is misleading because there isnt enough pets on the graph or data on the graph. 3. i honestly dont quite understand the question i would need to see it in person. Hope the first two answers help you out :-)
5 0
3 years ago
10. A bag contains 4 red balls, 6 green balls and some white balls. If the probability of not drawing a white ball in one draw b
klasskru [66]

Answer:

No of white balls = 5

Step-by-step explanation:

Given that,

Total no of red balls = 4

Total no of green balls = 6

The probability of not drawing a white ball in one draw be, P=\dfrac{2}{3}

We need to find the number of white balls. Let there are x balls.

The probability of drawing a white ball = 1 - the probability of not drawing a white ball

= 1 -2/3

= 1/3

Using the formula for solving probability of having a white ball.

P=\dfrac{\text{favorable outcome}}{\text{total no of outcomes}}\\\\\dfrac{1}{3}=\dfrac{x}{4+6+x}\\\\\dfrac{1}{3}=\dfrac{x}{10+x}\\\\10+x=3x\\\\10=2x\\\\x=5

Hence, there are 5 white balls.

3 0
3 years ago
Please help me!!!!!!
UkoKoshka [18]

Answer:

D

Step-by-step explanation:

because u have 5 potatoe bags and it .............

6 0
3 years ago
Write an equation of the line that passes through (6,-10) and is perpendicular To the line that passes through 4,-6) and (3,-4)
iVinArrow [24]

Answer:

all work is shown and pictured

7 0
3 years ago
What is (30 1/9 + 4 1/3) - 19 5/6
weqwewe [10]
14 11/18
I got this answer by doing 30 1/9 + 4 1/3= 34 4/9
Now I subtracted 34 4/9 by 19 5/6 to get the answer 14 11/18
TIP: When adding/subtracting/multiplying/dividing mixed numbers change them to an improper fraction first by multiplying the denominator and the whole number then adding the numerator
5 0
3 years ago
Other questions:
  • Determine the intercepts of the line. y=6x+13y=6x+13
    14·1 answer
  • Which number line represents all the values of x for the question x (2) = 49
    8·1 answer
  • Solve the following system of equations:
    12·1 answer
  • in 2 h, kelly laid new floor tile over 1/5 of the room. when she was joined by annette, the rest of the work was completed in 3h
    13·1 answer
  • Consider the points R and S in the figure. How many different lines pass through both R and S? Explain.
    13·1 answer
  • What is the sum of 2/7 and 3/9?​
    12·1 answer
  • Which of the following rigid motions is used to prove that vertical angle pairs are congruent? (1) a rotation by 90 about the i
    12·1 answer
  • HELP ME PLEASE I NEED HELP
    5·1 answer
  • (4x²y³ + 2xy² – 2y) – (–7x²y³ + 6xy² – 2y)<br> Find the difference of polynomials ?
    14·1 answer
  • One year membership cost $538. There is an initial sign up fee of $35. Write an equation you can use to find out how much you pa
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!