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SADC Course in Statistics Review and further practice (Session 10)

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To put your footer here go to View > Header and Footer 2 Learning Objectives At the end of this session you will be able to: compute probabilities associated with Venn diagrams, and the binomial, Poisson and normal distributions have greater confidence in explaining the differences and links between the normal, binomial and Poisson distributions Identify data arising in applications as being suited to the binomial, Poisson or normal models

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To put your footer here go to View > Header and Footer 3 Review of the three distributions Binomial distribution is appropriate when there is a sequence of Bernoulli trials, i.e. trials with just 2 possible outcomes, and interest is in looking at the number of successes (say r) in n trials Poisson distribution is suitable with data in the form of counts The normal distribution applies with many naturally occurring variables of a continuous nature, e.g. heights, weights, etc

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To put your footer here go to View > Header and Footer 4 Some general features The binomial and Poisson are discrete distributions, while the Normal corresponds to a continuous distribution Binomial takes values from 0 to n, Poisson can take values 0, 1, 2, …. etc., while a normally distributed variable can any value from - to + For large sample sizes, the Binomial and Poisson can be approximated by the Normal distribution

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To put your footer here go to View > Header and Footer 5 Parameters of the distributions The binomial is described by two parameters, namely n, the number of trials, and p, the probability of a success. The Poisson distribution is described by a single parameter. This is also the mean of the distribution. The normal distribution is described by two parameters, i.e. and. Here is the mean of the distribution, while is the standard deviation.

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To put your footer here go to View > Header and Footer 6 Poisson approx n to Binomial A binomial distribution with parameters n and p can be approximated by a Poisson distribution with parameter = np if n is large and p is small. The approximation gets better the bigger n becomes and smaller p becomes, but generally good when n>50 and p<0.1. This result is useful because for the normal approximation to hold, n has to be very large to compensate for small p. Approximation of binomial by normal is best around p=0.5 because of symmetry.

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To put your footer here go to View > Header and Footer 7 Identifying the distribution In statements below, what is the likely distribution for the key variable? An asset based poverty index has been produced for classifying each HHs as very poor or not. In a given rural area with 2475 HHs, the number of poor HHs is recorded. In a health survey, a record is made of the number of episodes of diarrhoea in the HH over a period of 3 months. Also recorded in this survey is the weight of children under 1 year and mothers age.

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To put your footer here go to View > Header and Footer 8 Practice with probabilities and dist ns The remainder of this session is devoted to practical work concerning probability concepts and probability distributions. You are encouraged to ask questions and ensure that ideas and concepts covered in the previous have been understood.

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To put your footer here go to View > Header and Footer 9 Practical work concerning all three distributions follows …

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6 6.1 - One Sample M ean μ, Variance σ 2, Proportion π 6 6.2 - Two Samples M eans, Variances, Proportions μ1 vs. μ2 σ12 vs. σ22 π1 vs. π2 6 6.3 - Multiple.

6 6.1 - One Sample M ean μ, Variance σ 2, Proportion π 6 6.2 - Two Samples M eans, Variances, Proportions μ1 vs. μ2 σ12 vs. σ22 π1 vs. π2 6 6.3 - Multiple.

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