Study Guides (248,578)
Canada (121,621)
Statistics (161)
STAT 230 (18)
Midterm

12W-Test5-soln.pdf

3 Pages
145 Views

School
Department
Statistics
Course
STAT 230
Professor
Changbao Wu
Semester
Winter

Description
1. In a quality control inspection items are classi▯ed as having a minor defect, a major defect, or as being acceptable. A carton of 10 items contains 2 with minor defects, 1 with a major defect, and 7 acceptable. Three items are chosen at random from the carton without replacement. Let X be the number selected with minor defects and Y be the number with major defects. [2] (a) Find the joint probability function f(x;y) of (X;Y ). ▯ 2▯ 1▯ 7 ▯ x y 3▯x▯y f(x;y) = ▯ ▯ ; x = 0;1;2; y = 0;1: 10 3 [2] (b) Find the marginal probability function of X. The marginal probability is hypergeometric: ▯2▯▯ 8 ▯ x 3▯x f 1x) = ▯ ▯ ; x = 0;1;2: 10 3 [2] (c) Find the probability P(X = 1 j Y = 0). 2 1 7 (1)(0)(2) f(1;0) 10 1 P(X = 1 j Y = 0) = = ( 3 = f (0) ( )( ) 2 2 0103 ( 3 2. Jane and Jack each toss a fair coin twice. Let X be the number of heads Jane obtains and Y be the number of heads Jack obtains. De▯ne U = X + Y and V = X ▯ Y . [2] (a) Find the mean and variance of V . X ▯ Bi(2;0:5), Y ▯ Bi(2;0:5), E(X) = E(Y ) = 1, V ar(X) = V ar(Y ) = 0:5, X and Y are independent. E(V ) = E(X) ▯ E(Y ) = 0; V ar(V ) = V ar(X ▯ Y ) = V ar(X) + V ar(Y ) = 1: [2] (b) Find Cov(U;V ). Cov(U;V ) = Cov(X + Y;X ▯ Y ) = Cov(X;X) ▯ Cov(X;Y ) + Cov(X;Y ) ▯ Cov(Y;Y ) = V ar(X) ▯ V ar(Y )
More Less

Related notes for STAT 230
Me

Log In

OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view

OR

By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.

Request Course
Submit