{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

homework_3_2005

# homework_3_2005 - 0.0 0.0 ≤ 5 1 12 32 31 19 21 0.3 0.2...

This preview shows pages 1–2. Sign up to view the full content.

Homework Set #3 Problem 1 Read Application Example 8 and do Problem 8.1. Problem 2 The way MIT admits undergraduate students is exemplified in the following table. Each applicant is rated to a discrete “scholastic index” X (horizontal axis) and a discrete “personal rating index” Y (vertical axis). The top number in each cell ( in bold ) is the number of applicants is a given year with the associated combination. The bottom number in each cell ( in italic ) is the probability of being accepted. (Although this is indeed the way MIT handles applications, all numbers are fictitious). Scholastic Index, X Personal Rating, Y 90-100 80-90 70-80 60-70 50-60 50 10 20 40 52 32 10 6 1.0 0.9 0.7 0.5 0.4 0.3 9 60 110 150 192 47 17 0.9 0.7 0.5 0.4 0.3 0.2 8 86 215 305 351 87 62 0.7 0.5 0.4 0.3 0.2 0.1 7 39 173 250 192 102 53 0.5 0.4 0.3 0.2 0.1 0.0 6 17 54 118 152 97 68 0.4 0.3 0.2 0.1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 0.0 0.0 ≤ 5 1 12 32 31 19 21 0.3 0.2 0.1 0.0 0.0 0.0 (a) Plot the marginal PMF of the two indices. (b) Plot the conditional PMFs of (X|Y = 8) and (X|Y = 6). (c) Plot the conditional PMF of (Y|X ≤ 50). (d) What is the probability that an applicant with Y = 7 is accepted. (e) Are X and Y independent? Why? Problem 3 In Bounty Town, U.S.A., total precipitation during the crop-growing season, Q, has a uniform distribution between 2 and 4 inches. The total crop value \$ depends on Q in such a way that (\$|Q = q) has uniform distribution (in millions of dollars) between (2q – 1) and (2q + 1). Note that the possible values of (Q,\$) are inside the parallelepiped shaded in the figure below: 2q + 1 \$ 2q - 1 2 4 q (a) What is the joint PDF of Q and \$? (b) What is the marginal PDF of \$? (c) What value of \$ is exceeded on average every 5 years? Read Application Examples 7, 9 and 10. ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

homework_3_2005 - 0.0 0.0 ≤ 5 1 12 32 31 19 21 0.3 0.2...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online