Chapter4

# Chapter4 - 129 CHAPTER 4 Section 4.1 1. a. P(x 1) = ] 25 ....

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 129 CHAPTER 4 Section 4.1 1. a. P(x 1) = ] 25 . ) ( 1 2 4 1 1 2 1 1 = = = -x xdx dx x f b. P(.5 X 1.5) = ] 5 . 5 . 1 5 . 2 4 1 5 . 1 5 . 2 1 = = x xdx c. P(x &amp;gt; 1.5) = ] 438 . ) ( 16 7 2 5 . 1 2 4 1 2 5 . 1 2 1 5 . 1 = = = x xdx dx x f 2. F(x) = 10 1 for 5 x 5, and = 0 otherwise a. P(X &amp;lt; 0) = 5 . 5 10 1 = -dx b. P(-2.5 &amp;lt; X &amp;lt; 2.5) = 5 . 5 . 2 5 . 2 10 1 = -dx c. P(-2 X 3) = 5 . 3 2 10 1 = -dx d. P( k &amp;lt; X &amp;lt; k + 4) = ] 4 . ] ) 4 [( 10 1 4 10 4 10 1 =-+ = = + + k k dx k k x k k 3. a. Graph of f(x) = .09375(4 x 2 ) 3 2 1-1-2-3 0.5 0.0-0.5 x1 f(x1) Chapter 4: Continuous Random Variables and Probability Distributions 130 b. P(X &amp;gt; 0) = 5 . ) 3 4 ( 09375 . ) 4 ( 09375 . 2 3 2 2 = -=- x x dx x c. P(-1 &amp;lt; X &amp;lt; 1) = 6875 . ) 4 ( 09375 . 1 1 2 =--dx x d. P(x &amp;lt; -.5 OR x &amp;gt; .5) = 1 P(-.5 X .5) = 1 - --5 . 5 . 2 ) 4 ( 09375 . dx x = 1 - .3672 = .6328 4. a. ] 1 ) 1 ( ) ; ( 2 / 2 / 2 2 2 2 2 =--=-= = -- - q q q q x x e dx e x dx x f b. P(X 200) = --= 200 2 / 2 200 2 2 ) ; ( dx e x dx x f x q q q ] 8647 . 1 1353 . 200 2 / 2 2 = +--=-q x e P(X &amp;lt; 200) = P(X 200) .8647, since x is continuous. P(X 200) = 1 - P(X 200) .1353 c. P(100 X 200) = = 200 100 ) ; ( dx x f q ] 4712 . 200 100 000 , 20 / 2 --x e d. For x &amp;gt; 0, P(X x) = = -x dy y f ) ; ( q -x y dx e e y 2 / 2 2 2 q ] 2 2 2 2 2 / 2 / 1 q q x x y e e---=-= 5. a. 1 = ( 29 ] ( 29 8 3 3 8 2 3 2 2 3 ) ( = = = = -k k k dx kx dx x f x b. P(0 X 1) = ] 125 . 8 1 1 3 8 1 1 2 8 3 = = = x dx x c. P(1 X 1.5) = ] ( 29 ( 29 2969 . 1 64 19 3 8 1 3 2 3 8 1 5 . 1 1 3 8 1 5 . 1 1 2 8 3 =-= = x dx x d. P(X 1.5) = 1 - ] ( 29 [ ] 5781 . 1 1 64 37 64 27 3 2 3 8 1 5 . 1 3 8 1 5 . 1 2 8 3 =-=--= = x dx x Chapter 4: Continuous Random Variables and Probability Distributions 131 6. a. b. 1 = -= =-=--1 1 2 4 2 2 4 3 3 4 ] 1 [ ] ) 3 ( 1 [ k du u k dx x k c. P(X &amp;gt; 3) = 5 . ] ) 3 ( 1 [ 4 3 2 4 3 =-- dx x by symmetry of the p.d.f d. ( 29 367 . 128 47 ] ) ( 1 [ ] ) 3 ( 1 [ 4 / 1 4 / 1 2 4 3 4 / 13 4 / 11 2 4 3 4 13 4 11 =-=--= -du u dx x X P e. P( |X-3| &amp;gt; .5) = 1 P( |X-3| .5) = 1 P( 2.5 X 3.5) = 1 - 313 . 16 5 ] ) ( 1 [ 5 . 5 . 2 4 3 =--du u 7. a. f(x) = 10 1 for 25 x 35 and = 0 otherwise b. P(X &amp;gt; 33) = 2 . 35 33 10 1 = dx c. E(X) = 30 20 35 25 2 35 25 10 1 = = x dx x 30 2 is from 28 to 32 minutes: P(28 &amp;lt; X &amp;lt; 32) = ] 4 . 32 28 10 1 32 28 10 1 = = x dx d. P( a x a+2) = 2 . 2 10 1 = + a a dx , since the interval has length 2....
View Full Document

## Chapter4 - 129 CHAPTER 4 Section 4.1 1. a. P(x 1) = ] 25 ....

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online