Knowee
Questions
Features
Study Tools

Conditional distribution of Y given X = x, P(Y = y | X = x) is

Question

Conditional distribution of Y given X = x, P(Y = y | X = x) is

🧐 Not the exact question you are looking for?Go ask a question

Solution

The conditional distribution of Y given X = x, denoted as P(Y = y | X = x), is a probability distribution that measures the likelihood that the event Y = y will occur given that X = x has already occurred.

Here's a step-by-step explanation:

  1. Identify the events: In this case, we have two events. Event X = x has already occurred and we want to find the probability of event Y = y occurring.

  2. Understand the concept of conditional probability: Conditional probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(A | B), which reads as "the probability of A given B".

  3. Apply the formula: The formula for conditional probability is P(A | B) = P(A ∩ B) / P(B). In this case, it would be P(Y = y | X = x) = P(Y = y ∩ X = x) / P(X = x).

  4. Calculate the probabilities: To find the conditional distribution, you would need to calculate the probabilities for all possible values of Y given X = x.

  5. Interpret the results: The resulting probabilities represent the distribution of Y given that X = x. This can give you insights into how Y behaves when X is known to be a certain value.

This problem has been solved

Similar Questions

Conditional distribution

Show that if X has pmf p(x), thenE[h(X)E[Y |X]] = ∑xh(x)E[Y |X = x]p(x)

For each of the following pairs of random variables X and Y , the conditional distribution of Ygiven {X = x} is a named distribution, with parameters that may depend on x. For each pair:1i. Write down the conditional distribution of Y given {X = x}, including parameter(s).(2 marks each)ii. Find E (Y | X). (1 mark each)iii. Find E(Y ). (1 mark each)iv. Find Cov(X, Y ). (2 marks each)You do not need to find the marginal distributions of X and Y , which might not be nameddistributions.(a) Choose a number between 10 and 29, uniformly at random, and call that number X.Take a standard deck of 52 cards and lay them out in a row, face up. Using a pen, puta checkmark on the first X cards. Then turn the cards face down, shuffle throughly, anddraw 5 cards. Let Y be the number of marked cards you draw.

H(Y|X)=∑xp(x)H(Y|X=x)

y = |x| is function

1/1

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.