2. Suppose that X is a uniform random (a) Explain why Y = 1/X is a random variable. Hint: Your answer should involve the definition of "random va given in class, and the function g(x) = 1/x. donsity function fy (y) of Y.
2. Suppose that X is a uniform random (a) Explain why Y = 1/X is a random variable. Hint: Your answer should involve the definition of "random va given in class, and the function g(x) = 1/x. donsity function fy (y) of Y.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
![1. Suppose that P(@) is a probability distribution on a discrete sample spac
Let BC be an event with P(B) > 0. Show that oB(@) = P(@)/P(B)
probability distribution on B.
%3D
2. Suppose that X is a uniform random variable on 0,1].
(a) Explain why Y = 1/X is a random variable.
Hint: Your answer should involve the definition of "random variab
given in class, and the function g(x) = 1/x.
(b) Find the probability density function fy (y) of Y.
Note: Be sure to specify the value of fY y) for every y ER.
3. Select two uniformly random points A, B in the unit interval [0, 1]. Then "cu
the interval [O, 1] at the points A and B to form three separate lines, of lengt
m, M -m and 1-M, where m = min{A, B} and M = max{A, B}. Show th
with probability 1/4, the three lines can form a triangle.
[-
Hint 1: If any of the lines is longer than 1/2, it will not be possible (as th
other two will not be able to "reach"). Otherwise, a trianglejcan be formec
ifu this event with a certain subset of the unit square (0, 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67a79aa2-f715-406c-8bee-8178252bb86d%2F9d59a0dd-6d06-4873-b8f7-e49ec2da986c%2Fs8l1024_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Suppose that P(@) is a probability distribution on a discrete sample spac
Let BC be an event with P(B) > 0. Show that oB(@) = P(@)/P(B)
probability distribution on B.
%3D
2. Suppose that X is a uniform random variable on 0,1].
(a) Explain why Y = 1/X is a random variable.
Hint: Your answer should involve the definition of "random variab
given in class, and the function g(x) = 1/x.
(b) Find the probability density function fy (y) of Y.
Note: Be sure to specify the value of fY y) for every y ER.
3. Select two uniformly random points A, B in the unit interval [0, 1]. Then "cu
the interval [O, 1] at the points A and B to form three separate lines, of lengt
m, M -m and 1-M, where m = min{A, B} and M = max{A, B}. Show th
with probability 1/4, the three lines can form a triangle.
[-
Hint 1: If any of the lines is longer than 1/2, it will not be possible (as th
other two will not be able to "reach"). Otherwise, a trianglejcan be formec
ifu this event with a certain subset of the unit square (0, 1.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 5 images
Similar questions
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON