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
Neko [114]
3 years ago
11

We have two fair three-sided dice, indexed by i = 1, 2. Each die has sides labeled 1, 2, and 3. We roll the two dice independent

ly, one roll for each die. For i = 1, 2, let the random variable Xi represent the result of the i-th die, so that Xi is uniformly distributed over the set {1, 2, 3}. Define X = X2 − X1. 1. Calculate the numerical values of following probabilities:____________. (a) P(X = 0) = (b) P(X = 1) = (c) P(X = −2) = (d) P(X = 3) = Let Y = X2 . Calculate the following probabilities:_________. (a) P(Y = 0) =(b) P(Y = 1) = (c) P(Y = 2) =
Mathematics
1 answer:
Nikitich [7]3 years ago
8 0

Answer:

(a) P(X = 0) = 1/3

(b) P(X = 1) = 2/9

(c) P(X = −2) = 1/9

(d) P(X = 3) = 0

(a) P(Y = 0) = 0

(b) P(Y = 1) = 1/3

(c) P(Y = 2) = 1/3

Step-by-step explanation:

Given:

- Two 3-sided fair die.

- Random Variable X_1 : Result on 1st die.

- Random Variable X_2: Result on 2nd die.

- Random Variable X = X_2 - X_1.

Solution:

 

- Possible outcomes of X : { - 2 , -1 , 0 ,1 , 2 }

- The corresponding probabilities for each outcome are:

                 ( X = -2 ):  { X_2 = 1 , X_1 = 3 }  

                P ( X = -2 ):  P ( X_2 = 1 ) * P ( X_1 = 3 )  

                                :  ( 1 / 3 ) * ( 1 / 3 )  

                                : ( 1 / 9 )    

                ( X = -1 ):  { X_2 = 1 , X_1 = 2 } + { X_2 = 2 , X_1 = 3 }

                P ( X = -1 ):  P ( X_2 = 1 ) * P ( X_1 = 3 ) + P ( X_2 = 2 ) * P ( X_1 = 3)

                                :  ( 1 / 3 ) * ( 1 / 3 ) + ( 1 / 3 ) * ( 1 / 3 )

                                : ( 2 / 9 )        

 ( X = 0 ):  { X_2 = 1 , X_1 = 1 } + { X_2 = 2 , X_1 = 2 } +  { X_2 = 3 , X_1 = 3 }

               P ( X = -1 ):3*P ( X_2 = 1 )*P ( X_1 = 1 )

                                :  3*( 1 / 3 ) * ( 1 / 3 )

                                : ( 3 / 9 ) = ( 1 / 3 )        

                  ( X = 1 ):  { X_2 = 2 , X_1 = 1 } + { X_2 = 3 , X_1 = 2 }

               P ( X = 1 ): 2* P ( X_2 = 2 ) * P ( X_1 = 1 )

                                : 2* ( 1 / 3 ) * ( 1 / 3 )

                                : ( 2 / 9 )

                  ( X = 2 ):  { X_2 = 1 , X_1 = 3 }

                 P ( X = 2 ):  P ( X_2 = 3 ) * P ( X_1 = 1 )  

                                   :  ( 1 / 3 ) * ( 1 / 3 )  

                                   : ( 1 / 9 )                  

- The distribution Y = X_2,

                         P(Y=0) = 0

                         P(Y=1) =  1/3

                         P(Y=2) = 1/ 3

- The probability for each number of 3 sided die is same = 1 / 3.

You might be interested in
Expand.<br> Your answer should be a polynomial in standard form.<br> (x-3)(x-4)=
nekit [7.7K]

Answer:

Step-by-step explanation:

So, it's x*x+x*-3+-4*x+3*-3

That simplifies to x^2 - 7x + 12

5 0
3 years ago
Simplify the expression: 3(1 + 8b)
luda_lava [24]

Answer:3+24b

Step-by-step explanation:

3(1+8b)

3+24b

4 0
3 years ago
Roscoe is exchanging $ 121 for Euros for his upcoming trip to Germany. If $2 can be exchanged for 1.78 Euros,how many Euros will
olasank [31]
Answer is define variable
6 0
1 year ago
Pleas help me out here.
Amiraneli [1.4K]

Answer:

A and E

Step-by-step explanation:

The given problem shows a graph of a vertical line with an undefined slope, in which its equation is x = 3 (which matches Option A).

It is not considered a function because it has the same input for every given output.  This means that regardless of its y-coordinate, its corresponding x-coordinate will always be x = 3.  

The Vertical Line Test allows us to know whether or not a graph is actually a function. Remember that a function can only take on one output for each input. We cannot plug in a value and produce two output values.  Since the graph represents a vertical line, it automatically fails the vertical line test. Therefore, it is not a function.

Because it is not a function, Options B, C, and D are invalid answers.

Hence, the correct answers are Options A and E.

4 0
3 years ago
What is the y-intercept of y= -.25 + 2?
sp2606 [1]

Answer:

2 (if the -.25 has an x after it)

If not 1.75

4 0
3 years ago
Read 2 more answers
Other questions:
  • What is the measure of each interior angle in a regular 15-gon?
    7·2 answers
  • Helpppppppppppppppppp
    14·2 answers
  • A bag contains 120 marbles. Some are red and the rest are black. There are 19 red marbles for every black marble. How many red m
    11·2 answers
  • Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. f(x, y) = 2x2y,
    11·1 answer
  • You roll a number cube you roll a number greater than 3.find probability of each event write it as a decimal
    10·1 answer
  • Production engineers at a company believe that a modified layout on its assembly lines might increase average worker productivit
    6·1 answer
  • If I round the number 43,257,529 to 43,300,000 what place value did I round the number to
    15·1 answer
  • I need help please.
    10·1 answer
  • Help me pleaseeeee I need this quick
    13·1 answer
  • RIGHT ANSWER GETS BRAINLYEST
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!