Example class 6

# Example class 6 - Probability of success Exercise 1 Let x...

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The University of Hong Kong Department of Statistics and Actuarial Science STAT1301 Probability and Statistics I Example class 6 Random Variables Revision Discrete Random Variables: Discrete random variable takes on finite or a countable infinite number of values. Probability mass function Cumulative Distribution Function: a) Bernoulli random variable : often occur as indicator, it takes on the value of 1 or 0 according to whether a guess was a success or failure. b) Binomial distribution : n independent experiments are taken, with each result in a ‘success’ with probability (p) and a ‘failure’ with probability (1-p). c) Poisson distribution : n denotes the numbers of independent trails, p is the probability of ‘success’ trail, the expected mean is defined as The Poisson distribution is used to approximate the binomial distribution when we see Number of trials

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Unformatted text preview: Probability of success Exercise 1. Let x be a discrete random variable. Its mass function f(x) is tabulated below: X 1 2 3 4 f(x) 0.2 0.4 - 0.2 a) Compute f(3) b) Calculate the cdf F(x) of X for x=1, 2, 3, 4. What is the value of F(3.3)? 2. Traffic on a road is passing a point at rate of 300 vehicles per hour. Determine the probability that exactly 4 vehicles pass in a period of 30 seconds. Compare the results using the following. a) Binomial distribution b) Poisson distribution 3. n = 300, p = 0.007, what is the probability of exactly 6 success using binomial and Poisson distribution approximation? 4. The number of claims received per business day at an insurer’s office follows a Poisson distribution with a mean of 2.4. Determine the probability that there are two or more days in the next five business days with three or more claims each....
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Example class 6 - Probability of success Exercise 1 Let x...

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