Homework Answers
SOLUTION:-
(5) A random variable(X) is a measurable function of the possible outcomes of the sample space in an experiment and maps these outcomes into the set of real numbers called range space.
(6) The probability distribution of a random variable which maps domain sample space of events into their probability is called the probability or density or mass function. Probability mass function gives the distribution of probabilities of a random variable across all the possible outcomes so it is essential to finding the probability of any outcome.
(7) The Cumulative distribution function of a random variable is the probability that is used X will take a value less than or equal to X. CDF can be used to find probability of range of random variable. It can prove useful in case of finding probabilities such as "at most x=x0",etc.
Add Answer to:
(5) Define random variable. Why should we care about random variables? How are they used/useful? ...
(1) Consider the probability space 2 [0, 1. We define the probability of an event A Ω to be its length, we define a sequence random variables as follows: When n is odd Xn (u) 0 otherwise while, when...
(1) Consider the probability space 2 [0, 1. We define the probability of an event A Ω to be its length, we define a sequence random variables as follows: When n is odd Xn (u) 0 otherwise while, when n is even otherwise (a) Compute the PMF and CDF of each Xn (b) Deduce that X converge in distribution (c) Show that for any n and any random variable X : Ω R. (d) Deduce that Xn does not converge...
(2 points) Consider a random variable X that takes the values 0, 50, 100, 150, and...
(2 points) Consider a random variable X that takes the values 0, 50, 100, 150, and 200, each with probability 0.2. Let Y = |X − 100| be the (absolute) deviation of X from its average value 100. Compute the probability mass function (PMF) and cumulative distribution function (CDF) of Y . Explain.
Define the random variable Y = -2X. Determine the cumulative distribution function (CDF) of Y ....
Define the random variable Y = -2X. Determine the cumulative
distribution function (CDF) of Y . Make sure to completely specify
this function. Explain.
Consider a random variable X with the following probability density function (PDF): s 2+2 if –2 < x < 2, fx(x) = { 0 otherwise. This random variable X is used in parts a, b, and c of this problem.
2. Determine whether the function f(x) is a valid probability distribution (PMF) for a random variable...
2. Determine whether the function f(x) is a valid probability distribution (PMF) for a random variable with the range 0,1,2,3,4 12 f(x) = 30 3. Suppose X is a random variable with probability distribution (PMF) given by f( and a range of 0,1, 2. Find the distribution function (CDF) for X 6
1. (Hint: This pmf should look familiar) Random variables X and Y have joint probability mass...
1. (Hint: This pmf should look familiar) Random variables X and Y have joint probability mass function (IPMI): otherwise. (a) Find Fx,y(x, y), the joint cumulative distribution function (CDF) of X and Y. A graphical repre- sentation is sufficient: probably the best way to do this is to draw the x - y plane and label different regions with the value of Fx,y(x, y) in that region. (b) Let Z = X2 + Y2. Find the probability mass function (PMF)...
1. Suppose that X and Y are random variables that can only take values in the intervals 0 X 2 and...
1. Suppose that X and Y are random variables that can only take values in the intervals 0 X 2 and 0 Y 3 2. Suppose also that the joint cumulative distribution function (cdf) of X and Y, for 0 < 2 and 03 y 3 2, is as follows: Fy). 16 [5] (a) Determine the marginal cdf Fx(x) of X and the marginal cdf Fy () of Y [5] (b) Determine the joint probability density function (pdf) f(x, y)...
P7 continuous random variable X has the probability density function fx(x) = 2/9 if P.5 The...
P7
continuous random variable X has the probability density function fx(x) = 2/9 if P.5 The absolutely continuous random 0<r<3 and 0 elsewhere). Let (1 - if 0<x< 1, g(x) = (- 1)3 if 1<x<3, elsewhere. Calculate the pdf of Y = 9(X). P. 6 The absolutely continuous random variables X and Y have the joint probability density function fx.ya, y) = 1/(x?y?) if x > 1,y > 1 (and 0 elsewhere). Calculate the joint pdf of U = XY...
Define a random variable , and a new random variable Y, such that 1) Find the...
Define a random variable , and a new random variable Y, such that 1) Find the density function of Y.( Instruction: Find the the cumulative distribution function and the derivative it) 2) Find the expectation of Y for (Hint: look for its connection with normal distribution of random variable) T~erp(A) We were unable to transcribe this imageWe were unable to transcribe this image
please answer all and show working This is the whole question 2. (50 pts) Now, referring...
please answer all and show working
This is the whole question
2. (50 pts) Now, referring to the PMF that you found in Problem 1, you are asked to find mean and variance of the random variable X. (a) Find the mean of X. (25 pts) b) Find the variance of X. 1. (50 pts) There is a 5-digit binary number. Random variable X is defined as the number of O's in the binary number. (a) Draw the probability mass...
Two independent random variables X1 and X2 both follow UNIF(0, 1). Define Y = e X1X2 . Find the cumulative distribution function (CDF) or the probability density function (pdf) of Y . (You can choose...
Two independent random variables X1 and X2 both follow UNIF(0, 1). Define Y = e X1X2 . Find the cumulative distribution function (CDF) or the probability density function (pdf) of Y . (You can choose either one).
(1) Consider the probability space 2 [0, 1. We define the probability of an event A Ω to be its length, we define a sequence random variables as follows: When n is odd Xn (u) 0 otherwise while, when n is even otherwise (a) Compute the PMF and CDF of each Xn (b) Deduce that X converge in distribution (c) Show that for any n and any random variable X : Ω R. (d) Deduce that Xn does not converge...
Define the random variable Y = -2X. Determine the cumulative
distribution function (CDF) of Y . Make sure to completely specify
this function. Explain.
Consider a random variable X with the following probability density function (PDF): s 2+2 if –2 < x < 2, fx(x) = { 0 otherwise. This random variable X is used in parts a, b, and c of this problem.
2. Determine whether the function f(x) is a valid probability distribution (PMF) for a random variable with the range 0,1,2,3,4 12 f(x) = 30 3. Suppose X is a random variable with probability distribution (PMF) given by f( and a range of 0,1, 2. Find the distribution function (CDF) for X 6
1. (Hint: This pmf should look familiar) Random variables X and Y have joint probability mass function (IPMI): otherwise. (a) Find Fx,y(x, y), the joint cumulative distribution function (CDF) of X and Y. A graphical repre- sentation is sufficient: probably the best way to do this is to draw the x - y plane and label different regions with the value of Fx,y(x, y) in that region. (b) Let Z = X2 + Y2. Find the probability mass function (PMF)...
1. Suppose that X and Y are random variables that can only take values in the intervals 0 X 2 and 0 Y 3 2. Suppose also that the joint cumulative distribution function (cdf) of X and Y, for 0 < 2 and 03 y 3 2, is as follows: Fy). 16 [5] (a) Determine the marginal cdf Fx(x) of X and the marginal cdf Fy () of Y [5] (b) Determine the joint probability density function (pdf) f(x, y)...
P7
continuous random variable X has the probability density function fx(x) = 2/9 if P.5 The absolutely continuous random 0<r<3 and 0 elsewhere). Let (1 - if 0<x< 1, g(x) = (- 1)3 if 1<x<3, elsewhere. Calculate the pdf of Y = 9(X). P. 6 The absolutely continuous random variables X and Y have the joint probability density function fx.ya, y) = 1/(x?y?) if x > 1,y > 1 (and 0 elsewhere). Calculate the joint pdf of U = XY...
please answer all and show working
This is the whole question
2. (50 pts) Now, referring to the PMF that you found in Problem 1, you are asked to find mean and variance of the random variable X. (a) Find the mean of X. (25 pts) b) Find the variance of X. 1. (50 pts) There is a 5-digit binary number. Random variable X is defined as the number of O's in the binary number. (a) Draw the probability mass...
Most questions answered within 3 hours.
-
An object in front of a concave mirror has a real image that is
11.5 cm...
asked 4 minutes ago -
Consider the reaction, C3 H8 + O2 --> CO2 + H2O. How many
moles of O2...
asked 1 hour ago -
You and your opponent both roll a fair die. If you both roll the
same number,...
asked 2 hours ago -
In a study of the accuracy of fast food drive-through orders,
Restaurant A had 257 accurate...
asked 2 hours ago -
Identify and describe in detail the four categories of
institutions that could be included in a...
asked 2 hours ago -
In python
class Customer:
def __init__(self, customer_id, last_name, first_name, phone_number, address):
self._customer_id = int(customer_id)
self._last_name =...
asked 2 hours ago -
What is an example of a limitation in implementing a new
ERP system and how it...
asked 2 hours ago -
In a section of 9.7cm of an artery with a radius of 2.6mm there
is a...
asked 2 hours ago -
the two carboxylic acid groups of aspartic acid have different
acidities with pKa values of 2.1...
asked 2 hours ago -
Would CuCO3 aqueous salt combined with calcium chloride
form a solid precipitate? If so, what would...
asked 2 hours ago -
How do ECM Solutions assist in embedding a culture of continuous
improvement in an organization? (Project...
asked 2 hours ago -
Directions
These directions introduce the idea of Essential Questions.
Since this may be a new concept...
asked 2 hours ago