stat2303_tutorial02

E ie find the mean and variance of and

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Unformatted text preview: , , i.e. ~ , find the mean and variance of . √ , , and √ , then, 1 √2 1 √2 1 √2 1 √2 1 √2 Note that , then and, So, 1 Page 2 of 4 STAT2303 Probability Modelling/STAT2803 Stochastic Models Semester 1, 2010­11 3. Suppose , and are independent gamma random variables with parameters , respectively, i.e. and . Approach 1 (Moment Generating Function) Hence, ~ , , i.e. the pdf of T is Γ Approach 2 (Too time-consuming!) Γ Γ Γ Γ Γ Γ Page 3 of 4 , and . Derive the pdf of STAT2303 Probability Modelling/STAT2803 Stochastic Models Semester 1, 2010­11 4. Let and be independent exponential random variables with parameters respectively. , (a) Find the probability density function for For 0, , z z, Y 1 1 1 0, Hence, for , 1 1 (b) Calculate . , , 1 (c) If 2. , calculate 1 2 2 2 2 1 1 3 2 3 1 3 Page 4 of 4 and . z z Y z ,...
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This note was uploaded on 03/15/2014 for the course STAT 2303 taught by Professor Steven during the Fall '11 term at HKU.

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