Example Class 6

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

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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
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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 &gt; 0 . b. If ² ~ ¶· ( » , 2 ) and ¼ ~ µ½¾ ( ¿ ) , then µ ² &gt; ¿ 2 À = µ ( ¼ &lt; » ) ....
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Example Class 6 - outside this range are unusable. One...

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