{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# final - b at most 60 were minted in Philadelphia In each...

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

MAT 521 Final June 25, 2004 Instructions: Write the answers and show all your work in the blue books. There are 5 problems. Make sure you do all 5. No books, notes, or collaboration with others. (A Z-table is attached.) Problem 1. (6 points) Five balls are drawn without replacement from an urn containing 3 red balls, 6 black balls, and 1 yellow ball. a. Find the probability that the sample will contain balls of every available color. (Hint: complement rule and inclusion-exclusion.) b. Find the expected number of yellow balls in the sample. Problem 2. (9 points) Let X and Y have joint probability density function given by f ( x, y ) = 2 x y 2 , 0 < x < 1 , y 1 . a. Find the marginal density of Y . b. Find the probability density function of Y . c. Find P ( Y < 2 X ) . Problem 3. (6 points) 68% of all pennies produced in a certain year were coined at the Philadelphia Mint, 28% at the Denver Mint, and the rest at the San Francisco Mint. In a random sample of 100 pennies from the year in question estimate the probability that a. exactly 3 were minted in San Francisco;

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: b. at most 60 were minted in Philadelphia. In each case write (a) an expression for the exact (binomial) probability; and (b) the numerical result of either the Poisson or normal approximation, as ap-propriate. 1 Problem 4. (6 points) The moment generating function of X is given by φ ( t ) = 1 1 + t 2 . a. Find the variance of X. b. Find the moment generating function of 2 X + Y if X and Y are indepen-dent, identically distributed. (Hint: to handle the factor of 2, write down the deﬁnition of the moment generating function of X and replace X by 2 X there.) Problem 5 (3 points) Assume that pro golfers’ scores are normally dis-tributed with mean 70.5 and variance 4.3. After the ﬁrst day of play at a golf tournament the ﬁeld of 200 players will be downsized to 50 by cutting all those above a certain score. What is the highest cutoﬀ score that is likely to achieve this goal? 2...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

final - b at most 60 were minted in Philadelphia In each...

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

View Full Document
Ask a homework question - tutors are online