Chapter4.4_4.5 lecture notes

# Chapter4.4_4.5 lecture notes - Lecture notes Chapter 4...

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Lecture notes : Chapter 4 sections 4.4 and 4.5 SECTION 4.4. The Mean and Variance of a Probability Distribution 1. Definition of mean ( μ ) value of X . μ = allx x xf ) ( Example 1: An appliance dealer sells 3 different models of freezers having 10, 16 and 20 cubic feet of storage space, respectively. Let X= the amount of storage space purchased by the next customer and suppose the probability distribution for X is as follows: X 10 16 20 f(x) 0.3 0.5 0.2 Calculate μ 2(a ) Mean value of binomial distribution : np = μ i.e., n x 0 = Σ = μ x x n x p p x n - - ) 1 ( = np (b) Mean value of hypergeometric distribution μ = n(a/N) = np where p=a/N. EXAMPLE 2: Suppose that we choose n=100 individuals from a factory with N=400 individuals. Suppose also that 250 of the employees in the factory are male. Find the mean number of males if we choose these 100 individuals by sampling 100 (i) with replacement and (ii) without replacement. 3. Definition of variance ( σ 2 ) and standard deviation( σ ).
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