Example Class 6

# Example Class 6 - outside this range are unusable One...

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

The University of Hong Kong Department of Statistics and Actuarial Science STAT1801 Probability and Statistics: Foundations of Actuarial Science (10-11) Example Class 6 1. Customers arrive at a travel agency at a mean rate of 9 per hour in accordance with a Poisson process. Suppose the travel agency opens at 9:00 am. a. Find the probability that no customers arrived before 9:30 am. b. Find the probability that more than five customers arrived before 9:30 am. c. Find the probability that there were more than five customers arrived before 9:30 am, given that at least one customers arrived within that period. 2. Let ? ~ ± (0,1) and ² ~ ± (80,100) . Find the following probabilities, ³ or ´ . (A standard Normal table is given at the back of this page.) a. µ ( ? < 1.37) b. µ ( ? ≥ − 1.75) c. µ (75 < ² ≤ 85) d. µ (0 < ? < ´ ) = 0.379 e. µ (| ? | < ´ ) = 0.95 f. µ ( ² ≤ ³ ) = 0.95 3. A manufacturer needs washers between 0.1180 and 0.1220 inch thick; any thicknesses

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: outside this range are unusable. One machine shop sells washers at \$3.00 per 1000. Their thicknesses are normally distributed with a mean of 0.1200 inch and a standard deviation of 0.0010 inch. Another machine shop sells washers at \$2.60 per 1000. Their thicknesses are normally distributed with a mean of .1200 inch and a standard deviation of .0015 inch. Which shop offers a better deal? 4. Jim takes two papers X and Y in an examination. His score on X has a N (54,36) distribution and his score on Y has a N (66 , 64) distribution. He will pass the examination if his total score is 100 or above. What is his probability of passing the examination? Assume X and Y are independent. 5. Prove the following results: a. If ² ~ ¶· ( ¸ , ¹ ) , then º² ~ ¶· ( ¸ , ¹ º ) for any º > 0 . b. If ² ~ ¶· ( » , 2 ) and ¼ ~ µ½¾ ( ¿ ) , then µ ² > ¿ 2 À = µ ( ¼ < » ) ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

Example Class 6 - outside this range are unusable One...

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

View Full Document
Ask a homework question - tutors are online