Bundle

Probability and Statistics II

CHAPTER ONE 1.1. RANDOM VARIABLES One of the basic ideas in probability is that of a random variable. In many cases this is simply the numerical variable... [Show More]

14 Items

probability and statistics II week 14

BIVARIATE EXPECTATION There are many problems in which we are interested not only in the expected value of a random variable X, but also in the expected v... [Show More]

Class Notes
$16.95
0
77

probability and statistics II week 13

MARGINAL DISTRIBUTIONS Definition 5 If X and Y are discrete random variables and is the value of their joint probability distribution at , the function ... [Show More]

Class Notes
$15.45
0
96

probability and statistics II week 12

CHAPTER FOUR: BIVARIATE DISTRIBUTION THEORY We earlier defined random variable as a real-valued function over a sample space with a probability measure, a... [Show More]

Class Notes
$11.45
0
75

probability and statistics II week 11

From Equation (3.2.3), we see that the normal distribution has the cumulative distribution function , ……………………………………………... [Show More]

Class Notes
$12.45
0
77

probability and statistics II week 10

THE BETA DISTRIBUTION X is uniform on the interval [a, b], the p.d.f. of the uniform distribution is defined as: The uniform density is a special ca... [Show More]

Class Notes
$13.45
0
96

probability and statistics II week 9

3.1. UNIFORM DISTRIBUTIONS: SPECIAL PROBABILITY DENSITY FUNCTIONS In this section we shall study some of the probability densities that figure most promin... [Show More]

Class Notes
$10.45
0
83

probability and statistics II week 8

1.1.1. GEOMETRIC (PASCAL) DISTRIBUTION A random variable X is defined to have a geometric distribution, if the discrete probability distribution function ... [Show More]

Class Notes
$13.45
0
89

probability and statistics II week 7

Example 3.1 Given , p = probability of success and q is the probability of failure. Show that f (x) is a discrete probability density function (p. d.... [Show More]

Class Notes
$10.45
0
102

probability and statistics II week 6

CHAPTER THREE: UNIVARIATE DISTRIBUTIONS 1.1. DISCRETE DISTRIBUTIONS In this chapter we shall study some of the probability distributions that figure m... [Show More]

Class Notes
$10.45
0
81

probability and statistics II week 5

2.4. MOMENT GENERATING FUNCTION (m.g.f) The moment generating function (m.g.f) of a random variable X is defined as: is the expected value of . We... [Show More]

Class Notes
$10.45
0
101

probability and statistics II week 1

CHAPTER ONE 1.1. RANDOM VARIABLES One of the basic ideas in probability is that of a random variable. In many cases this is simply the numerical variable... [Show More]

Class Notes
$10.45
0
116

probability and statistics II week 2

There are many problems in which it is of interest to know the probability that the value of a random variable is less than or equal to some real number x.... [Show More]

Class Notes
$10.45
0
116

probability and statistics II week 3

As in the discrete case, there are many problems in which it is of interest to know the probability that the value of a continuous random variable X is les... [Show More]

Class Notes
$10.45
0
84

probability and statistics II week 4

Properties of Expectation Let X be a random variable and c a constant. Then we have: (i) E (c) = c, for c a constant (ii) E [c g (x)] = c E [g (x)], w... [Show More]