A First Course in Probability
A First Course in Probability
9th Edition
ISBN: 9780321794772
Author: Sheldon Ross
Publisher: PEARSON
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Chapter 6, Problem 6.18P

Let X 1 and X 2 be independent binomial random variables with X i having parameters ( n i , p i ) , i = 1 , 2 . Find

a. P ( X 1 X 2 = 0 ) ;

b. P ( X 1 + X 2 = 1 ) ;

c. P ( X 1 + X 2 = 2 ) .

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Question 1: Let X be a random variable with p.m.f (|x| +1)² x= -2, -1, 0, 1,2 f(x) = C 0, O.W 1. The value of c. 2. The c.d.f. 3. E(X). 4. E(2x+3). 5. E(X²). 6. E(3x²+4). 7. E(X(3X+4)). 8. Var(X). 9. Var (6-3X). 10. Find the m.g.f of the random variable X
Please could you explain how to do integration by parts for this question in detail please
2. Claim events on a portfolio of insurance policies follow a Poisson process with parameter A. Individual claim amounts follow a distribution X with density: f(x)=0.0122re001, g>0. The insurance company calculates premiums using a premium loading of 45%. (a) Derive the moment generating function Mx(t).
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