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
tatyana61 [14]
3 years ago
6

A random variableX= {0, 1, 2, 3, ...} has cumulative distribution function.a) Calculate the probability that 3 ≤X≤ 5.b) Find the

expected value of X, E(X), using the fact that. (Hint: You will have to evaluate an infinite sum, but that will be easy to do if you notice that
Mathematics
1 answer:
olchik [2.2K]3 years ago
8 0

Answer:

a) P ( 3 ≤X≤ 5 ) = 0.02619

b) E(X) = 1

Step-by-step explanation:

Given:

- The CDF of a random variable X = { 0 , 1 , 2 , 3 , .... } is given as:

                    F(X) = P ( X =< x) = 1 - \frac{1}{(x+1)*(x+2)}

Find:

a.Calculate the probability that 3 ≤X≤ 5

b) Find the expected value of X, E(X), using the fact that. (Hint: You will have to evaluate an infinite sum, but that will be easy to do if you notice that

Solution:

- The CDF gives the probability of (X < x) for any value of x. So to compute the P (  3 ≤X≤ 5 ) we will set the limits.

                   F(X) = P ( 3=

- The Expected Value can be determined by sum to infinity of CDF:

                   E(X) = Σ ( 1 - F(X) )

                   E(X) = \frac{1}{(x+1)*(x+2)} = \frac{1}{(x+1)} - \frac{1}{(x+2)} \\\\= \frac{1}{(1)} - \frac{1}{(2)}\\\\= \frac{1}{(2)} - \frac{1}{(3)} \\\\=  \frac{1}{(3)} - \frac{1}{(4)}\\\\= ............................................\\\\=  \frac{1}{(n)} - \frac{1}{(n+1)}\\\\=  \frac{1}{(n+1)} - \frac{1}{(n+ 2)}

                   E(X) = Limit n->∞ [1 - 1 / ( n + 2 ) ]  

                   E(X) = 1

You might be interested in
You have two cards with a sum of (-12) in your hand. what two cards could you hsve
kirill115 [55]

The way the question is written, you could have almost anything in your hand. All they have to do is add to - 12.

-14 and 2

- 11 and - 1

-12 and 0

- 82 and 70

4 0
3 years ago
Adam works at a bakery. He uses 1/8 of his flour supply to make bread and 3/4 of his flour supply to make other baked goods. If
kykrilka [37]

Answer: B  

he has 24 in his supply!

Step-by-step explanation:

7 0
3 years ago
Dolbear's law states the relationship between the rate at which Snowy Tree Crickets chirp and the air temperature of their envir
Shtirlitz [24]
For this case, the first thing we are going to do is rewrite the equation correctly.
 We have then:
 T = 50 + (N-40) / 4
 We substitute the value of N = 98, we have then:
 T = 50 + (98-40) / 4
 T = 64.5 degrees Fahrenheit.
 Answer:
 the temperature in degrees Fahrenheit, T is:
 T = 64.5 degrees Fahrenheit.
5 0
3 years ago
An isosceles trapezoid is a quadrilateral with two congruent legs, a pair of parallel bases, and congruent base angles. Prove th
seraphim [82]

Answer:

The answer is below

Step-by-step explanation:

We must first define the concepts a little:

We have that when the sides are congruent that is to say that they have the same direction and the same size and also the two opposite sides are parallel, the angles will be the same.

Now, in an isosceles triangle, two angles are congruent, because their two sides are congruent.

3 0
3 years ago
An inverted pyramid is being filled with water at a constant rate of 25 cubic centimeters per second. The pyramid, at the top, h
UNO [17]

Answer:

\frac{225}{16} cm/s

Step-by-step explanation:

We are given that

\frac{dV}{dt}=25cm^3/s

Side of base=4 cm

l=w=4 cm

Height,h=12 cm

We have to find the rate at which the water level rising when the water level is 4 cm.

Volume of pyramid=\frac{1}{3}lwh=\frac{1}{3}l^2h

\frac{l}{h}=\frac{4}{12}=\frac{1}{3}

l=\frac{1}{3}h

Substitute the value

V=\frac{1}{27}h^3

Differentiate w.r.t t

\frac{dV}{dt}=\frac{3}{27}h^2\frac{dh}{dt}

Substitute the values

25=\frac{1}{9}(4^2)\frac{dh}{dt}

\frac{dh}{dt}=\frac{25\times 9}{16}=\frac{225}{16} cm/s

5 0
3 years ago
Other questions:
  • Can somebody explain this please
    14·1 answer
  • How would you write an equation of the line with the points (-2,4) (4,1)
    14·1 answer
  • What is 8 hours and 37 minutes in seconds?
    7·2 answers
  • A word form for 10,007,000,000,000
    7·1 answer
  • find the area of the regular decagon if the apothem is 5 inches and a side is 3.2 inches. Round to the nearest whole number
    9·1 answer
  • What is the median value of the data set shown on the line plot?
    15·2 answers
  • How to Include the decimal approximation of the irrational number to the nearest hundredth
    15·1 answer
  • How to find the limit
    9·1 answer
  • The hardest question i came across<br> 1+1<br> A.idk<br> B.5<br> C.2<br> D.69
    5·1 answer
  • ( x - 7 )/ ( x - 2 ) = 5/4 , Therefore x = -------------
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!