Solution to HW 10 - Solutions to EE351K homework assignment...

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Unformatted text preview: Solutions to EE351K homework assignment 10 1. a. 2 1 1 ( ) ( ) | ( ) | | 1 1 (1 ) Y s s s d d E Y M s ds ds s s = = = = = = =-- 2 2 2 2 2 3 1 2 ( ) ( ) | ( ) | | 2 1 (1 ) Y s s s d d E Y M s ds ds s s = = = = = = =-- 3 3 3 3 3 4 1 6 ( ) ( ) | ( ) | | 6 1 (1 ) Y s s s d d E Y M s ds ds s s = = = = = = =-- b. Since X and Y are independent, and W=X+Y, then 5 1 ( ) ( ) ( ) (1 ) W X Y M s M s M s s = =- 2 2 2 2 2 5 7 1 30 ( ) ( ) | ( ) | | 30 (1 ) (1 ) W s s s d d E W M s ds ds s s = = = = = = =-- 2. Consider Kn as the sum of n random variables, each of which is a Bernoulli trial with mean 0.2 and standard deviation 0.4. Hence Kn has mean 0.2n and standard deviation 0.4 n a. 100 ( ) 20 E K = b. 100 4 K = c. 100 100 20 18 20 ( 18) ( ) 1 ( 0.5) (0.5) 0.6915 4 4 K P K P-- = = - - = = d. 100 100 20 (16 24) ( 1 1) (1) ( 1) 2 (1) 1 0.6826 4 K P K P- =- - - = - = 3. a. Each bird follows a uniform distribution to land on a spot in the 100 span. Suppose they...
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Solution to HW 10 - Solutions to EE351K homework assignment...

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