title: Finite Mathematics Introductory Probability and Statistics
author: Dale Width
description: This is an introduction to Statistics and probability written by Dale Width, a Central Washington University math professor. It includes a solutions manual along with the book.
zlib_text:  
  129 
  CHAPTER 4 
   
  Section 4.1 
   
  1. 
   
  a. 
  P(x ≤ 1) = 
  ]
  25
  .
  )
  (
  1
  0
  2
  4
  1
  1
  0 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 > 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 < 0) = 
  5.
  0
  5 10
  1
  =
  ∫−
  dx
   
   
  b. P(-2.5 < X < 2.5) = 
  5.
  5.2
  5.2
  10
  1
  =
  ∫−
  dx
   
   
  c. 
  P(-2 ≤ X ≤ 3) = 
  5.
  3
  2 10
  1
  =
  ∫−
  dx
   
   
  d. P( k < X < 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 – x2)  
   
  3
  2
  1
  0
  -1
  -2
  -3
  0.5
  0.0
  -0.5
  x1
  f(x1)
  
  Chapter 4:  Continuous Random Variables and Probability Distributions 
   
  130 
  b. P(X > 0) = 
  5.
  )
  3
  4
  (
  09375
  .
  )
  4
  (
  09375
  .
  2
  0
  3
  2
  0
  2
  =
  
  
  −
  =
  −
  ∫
  x
  x
  dx
  x
   
   
  c. 
  P(-1 < X < 1) = 
  6875
  .
  )
  4
  (
  09375
  .
  1
  1
  2
  =
  −
  ∫−
  dx
  x
   
   
  d. P(x < -.5 OR x > .5) = 1 – P(-.5 ≤ X ≤ .5) = 1 - ∫−
  −
  5
  .
  5.
  2)
  4
  (
  09375
  .
  dx
  x
   
   
   
   
   
    = 1 - .3672 = .6328 
   
   
  4