Exam 5: Some Important Discrete Probability Distributions

Instruction 5.3 There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: Returns Probability Neighbourhood A Neighbourhood B 0.25 -\ 22,500 \ 30,500 0.40 \ 10,000 \ 25,000 0.35 \ 40,500 \ 10,500 -Referring to Instruction 5.3,what is the variance of the gain in value for the house in neighbourhood A?

The number of customers arriving at a department store in a 5-minute period has a binomial distribution.

Instruction 5.3 There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: Returns Probability Neighbourhood A Neighbourhood B 0.25 -\ 22,500 \ 30,500 0.40 \ 10,000 \ 25,000 0.35 \ 40,500 \ 10,500 -Referring to Instruction 5.3,what is the total variance of value gain if you invest in both houses?

Instruction 5.7 A major airline keeps a record of the number of mishandled bags per 1,000 customers. In 2011, the airline had 4.06 mishandled bags per 1,000 customers. Assume that the number of mishandled bags has a Poisson distribution. -Referring to Instruction 5.7,what is the probability that in the next 1,000 customers,the airline will have more than five but less than eight mishandled bags?

Instruction 5.3 There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: Returns Probability Neighbourhood A Neighbourhood B 0.25 -\ 22,500 \ 30,500 0.40 \ 10,000 \ 25,000 0.35 \ 40,500 \ 10,500 -Referring to Instruction 5.3,if you can invest half of your money on the house in neighbourhood A and the remaining on the house in neighbourhood B,what is the portfolio expected return of your investment?

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year.The variance of the number of power outages is______

Instruction 5.6 The quality control manager of Marilyn's Biscuits is inspecting a batch of chocolate chip biscuits. When the production process is in control, the average number of chocolate chip parts per biscuit is 6.0. -Referring to Instruction 5.6,what is the probability that any particular biscuit being inspected has between 5.0 and 8.0 inclusive chip parts?

In a game called Taxation and Evasion,a player rolls a pair of dice.If on any turn the sum is 7,11 or 12,the player gets audited.Otherwise,she avoids taxes.Suppose a player takes five turns at rolling the dice.T - he probability that she gets audited once is ______.

Instruction 5.2 The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Perth. X 0 1 2 3 4 5 0.1 0.2 0.4 0.1 0.0 0.0 P(X) 0 0 5 5 5 5 -Referring to Instruction 5.2,the mean or expected value of the number of accidents is ______.

Binomial distribution has ______ properties.

Instruction 5.5 A certain type of new business succeeds 60% of the time. Suppose that three such businesses open (where they do not compete with each other, so it is reasonable to believe that their relative successes would be independent). -Referring to Instruction 5.5,the probability that all three businesses fail is ______

Instruction 5.3 There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: Returns Probability Neighbourhood A Neighbourhood B 0.25 -\ 22,500 \ 30,500 0.40 \ 10,000 \ 25,000 0.35 \ 40,500 \ 10,500 -Referring to Instruction 5.3,if you can invest 30% of your money on the house in neighbourhood A and the remaining on the house in neighbourhood B,what is the portfolio expected return of your investment?