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STAT1301 (T3 ques)

# STAT1301 (T3 ques) - THE UNIVERSITY OF HONG KONG DEPARTMENT...

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THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT 1301 PROBABILITY AND STATISTICS I EXAMPLE CLASS 3 1. A discrete random variable X has the following probability mass function ( pmf ): x 1 2 3 4 p( x ) k 3 k Suppose the cumulative distribution function ( cdf ) is F( x ). (a) What is the value of k ? (b) What is the value of F(2.5)? (c) What is the value of p(2.5)? (d) Calculate Pr (2.5 < x <5). (e) Sketch the pmf and the cdf of X ? 2. A set of 10 measurements is listed in ascending order as follows: 1.4, 1.2, 0.3, 2.5, 2.5, 3.2, 5.6, 6.8, 7.1, c . It is known that the variance is 10.31. (a) Find c . (b) Suppose 8 2 1 , , , x x x L is another set of 8 measurements with mean 2.4 and variance 7.52. Find the mean and variance of the combined set of 18 measurements. 3. ( Poker ) If it is assumed that all 52 C 5 poker hands are equally likely, what is the probability of being dealt (a) one pair? (This occurs when the cards have denominations a, a, b, c, d where a, b, c, and d are all distinct.) (b) two pairs? (This occurs when the cards have denominations a, a, b, b, c

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STAT1301 (T3 ques) - THE UNIVERSITY OF HONG KONG DEPARTMENT...

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