Solution Found!
Alvin throws darts at a circular target of radius r and is
Chapter , Problem 7(choose chapter or problem)
Alvin throws darts at a circular target of radius r and is equally likely to hit any point in the target. Let X be the distance of Alvin's hit from the center. (a) Find the PDF, the mean. and the variance of X. (b) The target has an inner circle of radius t. If X t, Alvin gets a score of S = 1/ X. Otherwise his score is S = O. Find the CDF of S. Is S a continuous random variable?
Questions & Answers
QUESTION:
Alvin throws darts at a circular target of radius r and is equally likely to hit any point in the target. Let X be the distance of Alvin's hit from the center. (a) Find the PDF, the mean. and the variance of X. (b) The target has an inner circle of radius t. If X t, Alvin gets a score of S = 1/ X. Otherwise his score is S = O. Find the CDF of S. Is S a continuous random variable?
ANSWER:Step 1 of 2
X is the distance of Alvin hit from the center here. The CDF for X is first obtained here as:
Therefore, this is differentiated to get the PDF as:
The mean here is computed as:
The second moment of X here is computed as:
Therefore 