distribution

# distribution - Distribution and sampling Discrete random...

This preview shows pages 1–10. Sign up to view the full content.

1 Distribution and sampling Discrete random variable Continuous random variable Sampling and central limit theorem.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 Random Variables A random variable is a numerical description of the outcome of an experiment. A mapping from event to a real value. A discrete random variable may assume either a finite number of values or a infinite sequence of values. (usually count data) A continuous random variable may assume any numerical value in an interval or collection of intervals. (e.g. time, distance, weight etc.)
3 Examples of Random Variables Experiment Our Interest Outcome (X) Flip 3 coins # of heads 2 Make 100 sales call # of sales 21 Manufacture a product Production time in minute 21.50

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
4 Discrete Probability Distributions The probability distribution for a random variable describes how probabilities are distributed over the values of the random variable. For a discrete random variable x , the probability distribution is defined by a probability function , denoted by f (x), which provides the probability for each value of the random variable. The required conditions for a discrete probability function are: f ( x ) > 0 f ( x ) = 1
5 Expected Value and Variance The expected value , or mean , of a random variable is a measure of its central location. Expected value of a discrete random variable: E (x ) = = xf (x) The variance summarizes the variability in the values of a random variable. Variance of a discrete random variable: Var(x) = 2 = (x - ) 2 f (x) It can be interpreted as the descriptive measure of dispersion among the values of the random variable over a large number of repeats of the experiments. The standard deviation , , is defined as the positive square root of the variance.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
6 Example Expected Value of a Discrete Random Variable What is the expected number of TV sets sold in a day? x f ( x ) xf ( x ) 0 .40 .00 1 .25 .25 2 .20 .40 3 .05 .15 4 .10 .40 1.20= E ( x ) The expected number of TV sets sold in a day is 1.2
7 The Binomial Probability Distribution Properties of a Binomial Experiment The experiment consists of a sequence of n identical trials. Two outcomes, success and failure , are possible on each trial. The probability of a success, denoted by p , does not change from trial to trial. The trials are independent . Our Interest is the number of successes occurring in n trials. Let x denotes the number of successes in n trials. x=0, 1, …, n

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
8 Examples of Binomial Process (Bernoulli) In all cases we are interested in the probability of x successes in the n trials . Experiment with n trials Outcome per trial Probability of Success p Success Failure Flip a coin Head Tail 0.50 Inspect a part Good Defective 0.95 Contact a customer Sale No sale 0.20 Telephone survey Response No response 0.30
9 Example: Evans Electronics Binomial Probability Distribution Evans is concerned about a low retention rate for employees. On the basis of past experience, management has seen a turnover of 10% of the hourly employees annually. Thus, for any hourly employees chosen at random, management estimates

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 59

distribution - Distribution and sampling Discrete random...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online