Two six-sided dice are rolled and the random variablex is the sum of the values produced by each die.a. List the possible outcomes for the variable x, determine the probability for each outcome, and calculate the expected value of x.b. Calculate the variance of x.c. Calculate the standard deviation of x.a. List the possible outcomes for the variable x. Choose the correct answer below.O A. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12ОВ. 1,2, 3, 4, 5, 6O C. 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12O D. 3, 4, 5, 6, 7, 8, 9, 10, 11Determine the probability for each outcome. Select the correct choice below and fill in the answer boxes to complete your choice.(Type integers or fractions.)O A. P(2) =, P(3) = P(4) =P(5) =, P(6) =, P(7)= P(8) =P(9) =P(10) = P(11)= P(12) =%3DO B. P(1)=P(2) =, P(3) = P(4) = P(5) =P(6) =P(7) = P(8) =P(10) =, P(11) =P(12) =O C. P(3) = P(4) = P(5) =P(6) =P(7) =P(8) =P(9) =P(10) =, P(11) =O D. P(1) =P(2) = P(3) = P(4) =P(5) = P(6)=Click to select your answer(s). o six-sided dice are rolled and the random variable x is the sum of the values produced by each die.ist the possible outcomes for the variable x, determine the probability for each outcome, and calculate the expected value of x.alculate the variance of x.alculate the standard deviation of x.A. P(2)=P(3)= P(4)=TP(5) = P(6) =P(7) =, P(8) = P(9) = , P(10) = . P(11)= |P(12) =3. P(1)=P(2)=P(3) =, P(4)=P(5) =, P(6) =P(7)=P(8) = , P(9) =P(10)= P(11)-P(12)=%3D%3DP(3) =P(4) =. P(5) =P(6) = P(7)=P(8) =, P(9) =P(10) =, P(11) =· P(1)=P(2) =P(3) = P(4) =, P(5) =P(6) = |%3Dlate the expected value of x.|(Type an integer or a decimal. Do not round.)culate the variance of x.(Simplify your answer.ulate the standard deviation of x.(Round to three decimal places as needed.)select your answer(s).

Solution: Given that , Two six -side dice are rolled and random variable x is the sum of the values…

Two six-sided dice are rolled and the random variable x is the sum of the values produced by each die. a. List the possible outcomes for the variable x, determine the probability for each outcome, and calculate the expected value of x. b. Calculate the variance of x. c. Calculate the standard deviation of x.

Two six-sided dice are rolled and the random variable x is the sum of the values produced by each die. a. List the possible outcomes for the variable x, determine the probability for each outcome, and calculate the expected value of x. b. Calculate the variance of x. c. Calculate the standard deviation of x.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

Two six-sided dice are rolled and the random variablex is the sum of the values produced by each die.
a. List the possible outcomes for the variable x, determine the probability for each outcome, and calculate the expected value of x.
b. Calculate the variance of x.
c. Calculate the standard deviation of x.
a. List the possible outcomes for the variable x. Choose the correct answer below.
O A. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
ОВ. 1,2, 3, 4, 5, 6
O C. 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
O D. 3, 4, 5, 6, 7, 8, 9, 10, 11
Determine the probability for each outcome. Select the correct choice below and fill in the answer boxes to complete your choice.
(Type integers or fractions.)
O A. P(2) =, P(3) = P(4) =
P(5) =, P(6) =
, P(7)= P(8) =
P(9) =
P(10) = P(11)= P(12) =
%3D
O B. P(1)=
P(2) =, P(3) = P(4) = P(5) =
P(6) =
P(7) = P(8) =
P(10) =, P(11) =
P(12) =
O C. P(3) = P(4) = P(5) =
P(6) =
P(7) =
P(8) =
P(9) =
P(10) =, P(11) =
O D. P(1) =
P(2) = P(3) = P(4) =
P(5) = P(6)=
Click to select your answer(s).

o six-sided dice are rolled and the random variable x is the sum of the values produced by each die.
ist the possible outcomes for the variable x, determine the probability for each outcome, and calculate the expected value of x.
alculate the variance of x.
alculate the standard deviation of x.
A. P(2)=
P(3)= P(4)=T
P(5) = P(6) =
P(7) =
, P(8) = P(9) = , P(10) = . P(11)= |
P(12) =
3. P(1)=
P(2)=
P(3) =, P(4)=
P(5) =, P(6) =
P(7)=
P(8) = , P(9) =
P(10)= P(11)-P(12)=
%3D
%3D
P(3) =
P(4) =. P(5) =
P(6) = P(7)=
P(8) =, P(9) =
P(10) =, P(11) =
· P(1)=
P(2) =
P(3) = P(4) =
, P(5) =
P(6) = |
%3D
late the expected value of x.
|(Type an integer or a decimal. Do not round.)
culate the variance of x.
(Simplify your answer.
ulate the standard deviation of x.
(Round to three decimal places as needed.)
select your answer(s).

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