Two percent of the parts from a production process are defective. A sample of five parts from the production process is selected. What is the probability that the sample contains exactly two defective parts?
Four percent of the customers of a mortgage company default on their payments. A sample of five customers is selected. What is the probability that exactly two customers in the sample will default on their payments?
The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3.
The probability that there are less than 3 occurrences is
Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected. The probability that there are no females in the sample is
Sixty percent of the student body of a large university consists of female students. A random sample of 8 students is selected. What is the random variable in this experiment?
Solution Summary
The solution provides step by step method for the calculation of binomial and Poisson probabilities. Formula for the calculation and interpretations of the results are also included.
Please use words to describe the solution, not just symbols. (basically, explain what is going on in addition to an answer) Use a math symbol editor where appropriate.
Problem 1:
Write a program to compute binomialprobabilities and compare the results with the Poisson approximation for the following cases:
a) P(X = 2)
Objective: Calculate binomial and Poissonprobabilities.
1) Chapter 5: Problem 5.5 (binomial)
Solve the following problems by using the binomial formula.
a. If n = 4 and p = .10 , find P(x = 3) .
b. If n = 7 and p = .80 , find P(x = 4) .
c. If n = 10 and p = .60 , find P(x ≥ 7) .
d. If n = 12 and p = .45
The random variable X has a Poisson distribution with a mean of 5. The random variable Y has a binomial distribution with n=X and p=1/2.
a) Find the mean and variance of Y.
b) Find P(Y=0)
A baseball team loses $10,000 for each consecutive day it rains, Say X, the number of consecutive days it rains at the beginning of the season, has a Poisson distribution with mean 0.2. What is the expected loss before the opening game?
An airline always overbooks if possible. A particular plane has 95 seats on a flight in wh
1. Compute the following and show your steps. 3! ÷ (0!*3!)
2. Three members of a club will be selected to serve as officers. The first person selected will be president, the second person will be vice-president and the third will be secretary/treasurer. How many ways can these officers be selected if there are 30 club memb
Examples of the binomial and Poisson distributions are all around us.
- Identify a real-life example or application of either the binomial or poisson distribution.
- Specify how the conditions for that distribution are met.
- Suggest reasonable values for n and p (binomial) or mu (poisson) for your example.
-
The Poisson distribution is given by the following
P(x,λ)=e ^ -λ * λ^x! x=0,1,2,3.....j.....
Where λ>0 is a parameter which is the average value μ in poisson distribution.
a) show that the maximum poisson probability P(x=j,λ) occurs at approximately the average value, that is λ=j if λ>1.
(hint: you can take t
1. A discrete random variable can have the values x =3
x=8, or x=10, and the respective probabilities are 0.2,
0.7, and 0.1. Determine the mean, variance, and standard
deviation of x.
2. According to the National Marine Manufacturers
Association, 50.0% of the population of Vermont were
boating participants during the m
Population of consumers where 30% of them favored a new product and 70% of them disliked it. If 20 persons are sampled, what are the probabilities of finding: Binomial: 8 or fewer consumers who favor the product. Precisely 10 consumers who favor the product. Fewer than 6 consumers who favor the product. More than 7 consumers who
Please do only 1, 2, 6, 7, 9, 10, 11.
1. Define (a) stochastic process; (b) random variable; (c) discrete random variable; and (d) probability distribution.
2. Without using formulas, explain the meaning of (a) expected value of a random variable; (b) actuarial fairness; and (c) variance of a random variable.
6. (a) Wha
