Q52 What is a probability density function and how is it relevant to the determination of...

Q52 What is a probability density function and how is it relevant to the determination of probabilities associated with a continuous random variable? [3 Marks]

DO NOT WRITE THE ANSWER - USE WORD FORMAT.

NO PLAGIARISM ACCEPTED IN THE ANSWER.

Expert Solution

The probability density function (PDF) is used for a continuous random variable rather than a discrete variable. We know that in a continuous random variable, there are infinite number of points, hence the absolute value of the likelihood that the the function will take a particular value of x will be 0. PDF is used where it tells us the relative likelihood of the point OR how much more likely that the function will take on a given value.

PDF can be used to find out the probability that the random variable will fall in a particular range of values. This can be found by integrating the pdf over the range which is the same as finding the area under the density function graph (within the range of-course).

The probability density function is non-negative because the probability cannot be negative, and the integral over the entire range/space is always equal to one.

orchestra answered 2 years ago

18. Joint Probability Calculations: a) What is a joint probability density function? i. What is an...

18. Joint Probability Calculations: a) What is a joint probability density function? i. What is an example of a discrete joint probability function? ii. What is an example of a continuous joint probability function? b) What are marginal density/mass distribution functions? How can we calculate them from the joint density/mass distribution functions? i. Can you calculate the marginals when the joint space is not a rectangle? (e.g. The space of jpdf[x,y] is 0 < x < y, 0 < y...

The random variables X and Y have the following probability density function (pdf). Conditional probability density...

The random variables X and Y have the following probability density function (pdf). Conditional probability density function is f(xly) = ax/y^2 , 0<x<y, 0<y<1 =0 , o/w marginal density finction is f(y) = by^4 ,0<y<1 = 0, o/w At this time, find the constant a and b values to be the probability density function, and then indicate whether the random variables X and Y are independent, and if not, indicate whether they are positive or inverse.

. The joint probability density function of X and Y is given by ?(?, ?) =...

. The joint probability density function of X and Y is given by ?(?, ?) = { ??^2? ?? 0 ≤ ? ≤ 2, 0 ≤ ?, ??? ? + ? ≤ 1 0 ??ℎ?????? (a) Determine the value of c. (b) Find the marginal probability density function of X and Y. (c) Compute ???(?, ?). (d) Compute ???(?^2 + ?). (e) Determine if X and Y are independent

1.Plotting densitiesPlot the probability mass function (pmf) or probability density function (pdf) for eachof the following...

1.Plotting densitiesPlot the probability mass function (pmf) or probability density function (pdf) for eachof the following scenarios:(a) Consider abinomialrandom variable,X.i. Plot the pmf ofX∼Bin(n= 10,p= 0.3).ii. Plot the pmf ofX∼Bin(n= 10,p= 0.7).iii. Plot the pmf ofX∼Bin(n= 100,p= 0.3).iv. What happens to the shape of the pmf ofX∼Bin(n,p) whenpgets larger?v. What happens whenngets larger?(b) Consider ageometricrandom variable,Y.i. Plot the pmf ofY∼Geom(p= 0.1).ii. Plot the pmf ofY∼Geom(p= 0.5).iii. Plot the pmf ofY∼Geom(p= 0.8).iv. What happens to the shape of the pmf ofY∼Geom(p)...

What is the difference between semiclassical probability density and classical probability density? Note: This is for...

What is the difference between semiclassical probability density and classical probability density? Note: This is for a quantum physics 2 course.

Give an example of a function F which is the joint probability distribution (not density) function...

Give an example of a function F which is the joint probability distribution (not density) function of a pair of random variables X and Y such that (a) X and Y are independent and discrete (b) X and Y are dependent and discrete (c) X and Y are independent and continuous (d) X and Y are dependent and continuous

1. What is the probability density function? 2. In the Business context, can anyone use an...

1. What is the probability density function? 2. In the Business context, can anyone use an example to show how the probability density function is applied in the real world?

Derive conditional expectation from joint probability density function.

The joint probability density function for two continuous random variables ?? and ?? is ??(??, ??)...

The joint probability density function for two continuous random variables ?? and ?? is ??(??, ??) = ??(3??2 − ??), 0 < ?? < 1, 0 < ?? < 1. Answer the following: (a) Find the value of ?? such that ??(??, ??) is a valid probability density function. (b) Find the marginal probability density function for ??, ??(??). (c) Find the marginal probability density function for ??, ??(??). (d) Find the conditional probability density function for ??|?? = ??,...

How do you do probability density function? Can you do this kind of question with a...

How do you do probability density function? Can you do this kind of question with a calculator? If so, then what are the commands to do said probability density function on said graph? Example question : The following density function describes a random variable X. f(x) = 1 - (x/2) if 0< x < 2

Question