Joint probability,-limit values

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In summary, The conversation is about finding the pdf of a function z and the integral limits needed for finding f(z) using marginal density. The person has solved most of the problem and is stuck at the end. They have attached the problem and their solution so far as a PDF. The limit of x is from z to 1 and the limit of y is from z/x to 1. The final calculation for Fz is z^2 - 2zlnz + 1.
  • #1
aruna1
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hello
i have given this problem to find pdf of function z.i have solved most of it and stuck at the end.
i have attached problem and my solution so far as pdf here.
what i want to know what are the integral limits for finding f(z) using marginal density (see the end the end of attached solution is it [0 to z] or [z to 1] ?)

thanks.
 

Attachments

  • Binder2c.pdf
    1.1 MB · Views: 217
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  • #2
start with
P(Z<=z)
=P(XY<=z)
=P(Y<=z/x), x not equals 0
from here we do double integration on pxy(x,y) to obtain area of Fxy(Y<=z/x)=1-P(Y>z/x)=Fz
The limit of x is from z to 1, limit of y is z/x to 1

Fz(z) my calculation z^2-2zlnz
 

What is joint probability?

Joint probability refers to the likelihood of two or more events occurring together. It is calculated by multiplying the individual probabilities of each event.

How is joint probability different from conditional probability?

Joint probability considers the likelihood of multiple events occurring together, while conditional probability focuses on the likelihood of an event occurring given that another event has already occurred.

What is the importance of joint probability in statistics?

Joint probability allows us to understand the relationship between multiple events and can help in making predictions and decisions based on these probabilities. It is a fundamental concept in statistics and is used in various fields such as finance, science, and engineering.

What are limit values in joint probability?

Limit values in joint probability refer to the upper and lower bounds of the probability of an event occurring. They are used to determine the likelihood of an event happening within a certain range of values.

How are joint probability and marginal probability related?

Marginal probability is the probability of a single event occurring, while joint probability is the likelihood of multiple events occurring together. Marginal probability can be calculated from joint probability by summing the probabilities of all possible outcomes for a single event.

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