Submitted By lthomas7832

Words 5569

Pages 23

Words 5569

Pages 23

CET4860

07/24/2014

Laboratory Number: _3_______ Examiner Name: Lawrence Thomas _exam 3______________

Date & Time Activity

|07/24/2014 |Received from National Lipid Processing Co. From Mr. Lard Fatback |

|0902 |A USB drive brand name PNY. |

| |Mr. Lard Fatback believes one of his former employee is trading Trade Secrets( Rodger Marks ) The company used a |

| |local examiner to image the drive .The company wants us to examine it and provide them with any information of |

| |investigate value |

| | |

| | |

|07/24/2014 | |

|0910 | |

| |FTK Imager 2.9.0 for drive is MP042011.E01 |

| |MDF5 checksum 5efe4fd057c8ec8a3ca010260e195bd |

| |SHA1 checksum 42e3447326ffeff0bc9e9cf5380a5763803dabc4 |

| |Acquisition started Tue Apr 26 11:17:16 2011…...

...variables X and Y are statistically independent if and only if f (x, y) = f (x) f (y) that is, if the joint PDF can be expressed as the product of the marginal PDFs. EXAMPLE 7 A bag contains three balls numbered 1, 2, and 3. Two balls are drawn at random, with replacement, from the bag (i.e., the ﬁrst ball drawn is replaced before the second is drawn). Let X denote the number of the ﬁrst ball drawn and Y the number of the second ball drawn. The following table gives the joint PDF of X and Y. X 1 1 Y 2 3 1 9 1 9 1 9 2 1 9 1 9 1 9 3 1 9 1 9 1 9 Now f ( X = 1, Y = 1) = 1 , f ( X = 1) = 1 (obtained by summing the ﬁrst column), and 9 3 f (Y = 1) = 1 (obtained by summing the ﬁrst row). Since f ( X, Y ) = f ( X )f (Y ) in this exam3 ple we can say that the two variables are statistically independent. It can be easily checked that for any other combination of X and Y values given in the above table the joint PDF factors into individual PDFs. It can be shown that the X and Y variables given in Example 4 are not statistically independent since the product of the two marginal PDFs is not equal to the joint PDF. (Note: f ( X, Y ) = f ( X )f (Y ) must be true for all combinations of X and Y if the two variables are to be statistically independent.) Continuous Joint PDF. The PDF f (x, y) of two continuous variables X and Y is such that f (x, y) ≥ 0 ∞ −∞ d c a ∞ −∞ b f (x, y) dx dy = 1 f (x, y) dx dy = P(a ≤ x ≤ b, c ≤ y ≤ d) Gujarati: Basic Econometrics, Fourth......

Words: 394375 - Pages: 1578

...variables X and Y are statistically independent if and only if f (x, y) = f (x) f (y) that is, if the joint PDF can be expressed as the product of the marginal PDFs. EXAMPLE 7 A bag contains three balls numbered 1, 2, and 3. Two balls are drawn at random, with replacement, from the bag (i.e., the ﬁrst ball drawn is replaced before the second is drawn). Let X denote the number of the ﬁrst ball drawn and Y the number of the second ball drawn. The following table gives the joint PDF of X and Y. X 1 1 Y 2 3 1 9 1 9 1 9 2 1 9 1 9 1 9 3 1 9 1 9 1 9 Now f ( X = 1, Y = 1) = 1 , f ( X = 1) = 1 (obtained by summing the ﬁrst column), and 9 3 f (Y = 1) = 1 (obtained by summing the ﬁrst row). Since f ( X, Y ) = f ( X )f (Y ) in this exam3 ple we can say that the two variables are statistically independent. It can be easily checked that for any other combination of X and Y values given in the above table the joint PDF factors into individual PDFs. It can be shown that the X and Y variables given in Example 4 are not statistically independent since the product of the two marginal PDFs is not equal to the joint PDF. (Note: f ( X, Y ) = f ( X )f (Y ) must be true for all combinations of X and Y if the two variables are to be statistically independent.) Continuous Joint PDF. The PDF f (x, y) of two continuous variables X and Y is such that f (x, y) ≥ 0 ∞ −∞ d c a ∞ −∞ b f (x, y) dx dy = 1 f (x, y) dx dy = P(a ≤ x ≤ b, c ≤ y ≤ d) Gujarati: Basic Econometrics, Fourth......

Words: 394375 - Pages: 1578