Exam 5: Some Important Discrete Probability Distributions

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year.The probability that there will be exactly 3 power outages in a year is______.

What type of probability distribution will most likely be used to analyse the number of cars with defective radios in the following problem? From an inventory of 48 new cars being shipped to local dealerships,corporate reports indicate that 12 have defective radios installed.The sales manager of one dealership wants to predict the probability out of the eight new cars it just received that,when each is tested,no more than two of the cars have defective radios.

Instruction 5.8 From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed. -Referring to Instruction 5.8,what is the probability out of the eight new cars it just received that,when each is tested,at least half of the cars have defective radios?

Suppose that past history shows that 6% of college students prefer Brand A cola.A sample of 10,000 students is to be selected.Which of the following distributions would you use to figure out the probability that at least half of them will prefer Brand A cola?

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 expected value gain for the house in neighbourhood A?

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 risk of your investment?

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 at least 6.0 chip parts?

The expected return of a two-asset portfolio is equal to the product of the weight assigned to the first asset and the expected return of the first asset plus the product of the weight assigned to the second asset and the expected return of the second asset.

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 standard deviation of the number of accidents is ______

The online access computer service industry is growing at an extraordinary rate.Current estimates suggest that only 20% of the home-based computers have access to online services.This number is expected to grow quickly over the next 5 years.Suppose 25 people with home-based computers were randomly and independently sampled. -Find the probability that fewer than 10 of those sampled currently have access to online services.

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 10% of your money on the house in neighbourhood A and the remaining on the house in neighbourhood B,what is the portfolio risk of your investment?

The covariance

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year.The probability that there will be between 1 and 3 inclusive power outages in a year is ______

Suppose that a judge's decisions follow a binomial distribution and that his verdict is correct 90% of the time.In his next 10 decisions,the probability that he makes fewer than 2 incorrect verdicts is 0.736.

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 eight mishandled bags?

The Poisson distribution can be used to approximate the binomial distribution under certain circumstances.

If p remains constant in a binomial distribution,an increase in n will increase the variance.

The number of 000 calls in Hobart has a Poisson distribution with a mean of 10.0 calls a day.The standard deviation of the number of 000 calls in a day 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 half of your money on the house in neighbourhood A and the remaining on the house in neighbourhood B,what is the portfolio risk of your investment?

Instruction 5.8 From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed. -Referring to Instruction 5.8,what is the probability out of the eight new cars it just received that,when each is tested,no more than two of the cars have defective radios?