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NamedDiscreteRVs

NamedDiscreteRVs - (5.4 Binomial Bernoulli Trial a single...

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(5.4) Binomial Bernoulli Trial: a single random experiment with outcome either success or failure. It has a success probability p. For example: Flipping a coin once where getting a head is a success Rolling a dice once and a success is rolling a 5 Having a child and a success is a girl If Y~Bernoulli(p=0.6) So failure probability is ______ For a Bernoulli Random Variable: P(X=x) = E(X) = Var(X) = Repeat Bernoulli trials 1. independent 2. success/failure for each trial 3. probability stays the same in all trials Binomial Random Variable : given the number of trials (10, 20, 6) you want to count the number of successes (H, 5’s, G) Number of heads in 10 flips of a coin Number of 5’s in 20 rolls Number of girls in 6 children where n=number of trials and p=prob of success

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Example : To test for ESP, we have 4 cards. They will be shuffled and one randomly selected each time, and you are to guess which card is selected. This is repeated 10 times. Let R be the number of times you guess a card correctly. 1. What are the distribution and parameters of R? 2. If someone were just guessing, did NOT have ESP, how many would you expect them to get right out of 10 tries? 3. What is the probability they guess half of them correctly? 4. What is the probability they get at least 3 correct? In General: If X~Binomial(n,p) P(X=x) = E(X) = Var(X) =
Example : An insurance company receives claims independently of one another for various incidents. Of these claims, 10% are claims for damages from vandalism. If the insurance company receives 20 claims, let V be the number of claims that are for vandalism. 1. What is the distribution and parameters of V? 2. What is the probability there are either 2 or 3 claims for vandalism? 3. If there are 4 or more claims for vandalism, the company must send you a special report so you can have the police check out the situation. What is the probability you have to send the police? 4. Given you didn’t get a special report, wha t is the probability the company received exactly 3 claims for vandalism? 5. In 20 claims, how many do you expect to be claims for vandalism? 6. What is the variance of number of vandalism claims received? 7. If 5 agents are filing claims (each 20 have 20 claims), how many total claims for vandalism do you anticipate?

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(5.5) Poisson Distribution Example: US population has 300 million people. We’ll ASSUME 1 in 10 million people are struck by lightning in a year and all of these strikes are independent of one another. Let L be the number of people in the US that are struck by lightning in a given year. 1. What are the distribution and parameters of L? 2. What is the probability that exactly 25 people will be struck by lightning in a given year? 3.
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NamedDiscreteRVs - (5.4 Binomial Bernoulli Trial a single...

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