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
iris [78.8K]
3 years ago
5

A) Let X be a random variable that can assume only positive integer values, and assume its probability function is P(X -n) A/3^n

for some constant A (n> 1). Find A.
b) Let X be a continuous random variable that can assume values between 0 and 3, and assume its density function is fx(x)- B(x2 +1) with some constant B (0< x ,3). Find B.
Mathematics
1 answer:
kramer3 years ago
5 0

Answer:

a) The value of A = 2

b) The value of B  = \dfrac{1}{12}

Step-by-step explanation:

a)

Given that:

X should be the random variable that assumes only positive integer values.

The probability function; P[X = n] = \dfrac{A}{3^n} for some constant A and n ≥ 1.

Then, let \sum \limits ^{\infty}_{n =1} P[X =n] = 1

This implies that:

A \sum \limits ^{\infty}_{n =1} \dfrac{1}{3^n}= 1

A \times  \dfrac{\dfrac{1}{3}}{1 - \dfrac{1}{3}} = 1

A \times  \dfrac{\dfrac{1}{3}}{\dfrac{2}{3}} = 1

A \times \dfrac{1}{2}=1

A = 2

Thus, the value of A = 2

b)

Suppose X represents a e constant A (n> 1). Find A.

b) Let X be a continuous random variable that can assume values between 0 and 3

Then, the density function of x is:

f_x(x) = \left \{ {{B(x^2+1)}   \ \ \ 0 \le x \le 3  \ \ \ \atop {0} \ \ \ otherwise} \right.

where; B is constant.

Then, using the property of the probability density function:

\int ^3_0 \ B (x^2+1 ) \ dx = 1\\

Taking the integral, we have:

B \Big [\dfrac{x^3}{3} +x \Big ]^3_0 = 1

B \Big [\dfrac{3^3}{3} +3 \Big ]= 1

B \Big [\dfrac{27}{3} +3 \Big ] = 1

B [ 9 +3 ] = 1

B [ 12 ] = 1

Divide both sides by 12

B  = \dfrac{1}{12}

You might be interested in
I'm really having trouble with this one. It says: Use your graphing calculator to find the value of f'(0) for f(x) = sin(x) + e^
lisov135 [29]

Step-by-step explanation:

f'(x) = d/dx [f(x)]

= d/dx (sinx + e^x) = cosx + e^x.

Therefore f'(0) = cos(0) + e^(0) = 2.

5 0
3 years ago
Exponential form of 81/625
Vesnalui [34]

Step-by-step explanation:

Hey, there!!

you number is: 81/625

We know that,

81=9×9

and

625=25×25

and............................................................

9×9 means 9^2

and 25×25 means 25^2

so, the exponential form of the question is,

=\frac{ {9}^{2} }{ {25}^{2} }

{we simply find exponential form by finding their fraction}

<em><u>Hope it helps</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em>

4 0
3 years ago
Are metals and non-metals good conductors true or false
andre [41]
False only metals are good conductors 
3 0
3 years ago
Read 2 more answers
Not drawn
Sveta_85 [38]

Answer:

Yes, It is a Right Triangle.

Step-by-step explanation:

The hypotenuse is the longest side of the triangle, so for this problem we set the hypotenuse's value to 18.2

From there it doesn't matter which side is which, as both will undergo the same operations.

If the following equation is true, then it is a right triangle.

7²+16.8²= 18.2²

49 + 282.24 = 331.24

The equation is True.

It is a right-angled Triangle.

6 0
3 years ago
In the diagram of circle O what is the measure of ABC
Olin [163]

Answer:

wheres the picture

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • Find the slope of the line that passes through the pair of points (1/10,6) and (3/16,11/5)
    12·1 answer
  • A closed cylindrical vessel contains a fluid at a 5MPa pressure. The cylinder, which has an outside diameter of 2500mm and a wal
    9·1 answer
  • How many 2/3 ounces portions each of saffron can Lily get from the 4 2/3 ounces of saffron she bought at the Union Market?
    13·1 answer
  • Five plus negative nineteen
    7·2 answers
  • Find the unit rate in feet per sec 240yards/1hour to feet per sec
    10·1 answer
  • Describe the likelihood of an event as impossible, unlikely, equally likely, likely or certain.
    15·1 answer
  • Earning an A in algebra this semester is an example of:
    6·2 answers
  • Help taking test plz
    11·2 answers
  • Question 16<br> 5 pts<br> Convert the Improper Fraction to a Mixed Number.<br> 45/12
    10·1 answer
  • Solve the formula r=4/3(p-q) for p
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!