hw03 - be tested one at a time(without replacement until...

This preview shows page 1. Sign up to view the full content.

ORIE 360/560 Fall 2007 Assignment 3 Due Tuesday, Sept. 18 at 2:00 pm Problem 1. In a certain engineering class every student receives a grade of 1.0, 2.0, 3.0, or 4.0., A student has a 30% probability of receiving a failing grade of 1.0 and a 70% probability of receiving a passing grade of 2.0 or higher. Among the students who pass, half receive 2.0, 30% receive 3.0, and the rest receive 4.0. Let X be the grade of a randomly selected student. Is X discrete, continuous, or mixed? Draw the cdf of X . Make sure to label your graph! Problem 2. Suppose X is a continuous random variable with density f ( x ) = ( ce - 3 x if 0 < x < 0 otherwise. (a) Find c . (b) Find P [ X > 3]. Problem 3. Let the point ( X, Y ) be uniformly distributed on an equilateral triangle with side length 1 unit. Find the probability that ( X, Y ) is at least 1/2 a unit of distance away from all three vertices of the triangle. Problem 4. A bin of 5 transistors is known to contain exactly 2 that are defective. The transistors are to
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: be tested one at a time (without replacement) until the defective one is identiﬁed. Let X be the number of tests made until the ﬁrst defective one is found (including the test that identiﬁes the ﬁrst defective one). Let Y be the number of additional tests up to and inlcuding the time that the second defective transistor is found. Find the joint pmf of ( X,Y ). The following problems are optional for students enrolled in 360, required for students enrolled in 560. Problem 5. Suppose X is uniformly distributed on the range [0 , 1]. Find the probability that X is irrational, ie, ﬁnd P [ X / ∈ Q ]. Problem 6. Again, suppose X ∼ U (0 , 1). Let Y n be the random variable given by Y n = 1 n d nX e , where d x e denotes the least integer k such that x ≤ k . (a) Find the distribution of Y n . (b) Find the distribution of Z n := Y n-X ....
View Full Document

• Fall '07
• EHRLICHMAN
• Probability distribution, Probability theory, Randomness, Discrete probability distribution, certain engineering class

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern