Chapter4.1-4.3 lecture notes

Chapter4.1-4.3 lecture notes - What is the probability of...

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AMS 310 Chapter 4.1, 4.2, 4.3 Random Variables: Definition: Assignment of a numerical value to an element or set of elements in the sample space. Terms: probability distributions: discrete random variable, continuous random variable probability histograms bar chart cumulative distribution function or distribution function. EXAMPLE Given that f(x)= k/2 x for x=0,1,2,3 and 4 = 0 otherwise. (a) find k (b)Find F(x) (c) Find an expression for F(x) (d) Draw a probability histogram and a (d) bar chart 4.2 The Binomial Distribution 1. Independent Bernouilli trials defined: (1) Two possible outcomes for each trial (2) The probability of success is the same for each trial (3) There are n trials and n is a constant . (4) The n trials are independent. 2. The binomial probability distribution = ) , ; ( p n x b x n x p p x n - - ) 1 ( for x=0,1,2….n. 3. Table 1 of values of cumulative probabilities for binomial distribution. x i p n x B 0 ) , ; ( = Σ = x n x p p x n - - ) 1 ( 4. Example : We toss a fair coin 10 times. What is the probability of exactly 5 heads?
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Unformatted text preview: What is the probability of less than 5 heads? What is the probability of more than 8 heads? 4.3 The Hypergeometric Distribution = ) , , ; ( N a n x h -- n N x n a N x a for x = 0,1 2,. .n x<a; n-x < N-a. 1.Hypergeometric distribution applies to sampling n from N without replacement. Bernouilli trials but not independent. 2, Hypergeometric probabilities are approximately equal to b(x; n , a/n) for n<N/10. Example: Three articles are selected from a lot of 10 articles of which 2 are defective and 8 are good by picking one at a time without replacement. Let X denote the number of defectives among the 3 drawn . Determine the probability distribution for X. What are the corresponding values if we sample without replacement?...
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This note was uploaded on 01/31/2008 for the course AMS 310.01 taught by Professor Mendell during the Fall '03 term at SUNY Stony Brook.

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