1. Darts: Alex, being bored since her friends from L3' are still doing Assignment 3, decides to play darts to pass the time to fill the void that doing 8 probability ques tions one day before the deadline had created. The dartboard is a unit circle centered at the origi n. Given that when Alex throws a dart, it lands uniformly on the dartboard and the coordinate it lands on is mapped by the pair of random variables (X, Y). (Remember that when X 0, Y 0), Alex hits at the center of the dartboard. a) Find the joint PDF. b) Find the marginal PDF for X c) required. Just answer and justi fication is sufficient). Find P(X > 0, Y > 0). (This question can be solved intuitively, excessive working is not
1. Darts: Alex, being bored since her friends from L3' are still doing Assignment 3, decides to play darts to pass the time to fill the void that doing 8 probability ques tions one day before the deadline had created. The dartboard is a unit circle centered at the origi n. Given that when Alex throws a dart, it lands uniformly on the dartboard and the coordinate it lands on is mapped by the pair of random variables (X, Y). (Remember that when X 0, Y 0), Alex hits at the center of the dartboard. a) Find the joint PDF. b) Find the marginal PDF for X c) required. Just answer and justi fication is sufficient). Find P(X > 0, Y > 0). (This question can be solved intuitively, excessive working is not
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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Transcribed Image Text:Darts: Alex, being bored since her friends from L3' are still doing Assignment 3, decides to
play darts to pass the time to fill the void that doing 8 probability questions one day before the deadline
1.
had created.
The dartboard is a unit circle centered at the origin. Given that when Alex throws a dart, it lands
uniformly on the dartboard and the coordinate it lands on is mapped by the pair of random variables
(X,Y). (Remember that when X = 0, Y = 0), Alex hits at the center of the dartboard.
a)
Find the joint PDF.
b)
Find the marginal PDF for X
c)
required. Just answer and justification is sufficient).
Find P(X > 0, Y > 0). (This question can be solved intuitively, excessive working is not
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