1. A two-horse race is about to take place. Horse A's finishing time X is uniformly distributed between 3 and 8minutes. Horse B's finishing time Y has a uniform distribution conditional on X, as follows:xfx₁x (y | x) = for = ≤ y ≤2x47x4a. Find the pdf of Y (HINT: define first fxy and the joint sample of X and Y).b. Find fxy(xly), the conditional pdf for X given Y.c. Are the event S=X ≤ Y and the random variable Y independent, i.e. is P(S|Y=y) = P(S)?What is the probability that the winner wins by less than 1 minute?Find the probability that the winning time is less than 6 minutes.d.e.

As per the guidelines of Bartleby, solution of only first 3 parts given.

Answered: A two-horse race is about to take…

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...

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