Discuss the below:
Q1. 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.
Q2. According to the National Marine Manufacturers Association, 50.0% of the population of Vermont were boating participants during the most recent year. For a randomly selected sample of 20 Vermont residents, with the discrete random variable x = the number in the sample who were boating participants that year, determine the following:
a E = x b. P(x
d. P( x = 12) e. P( 7 < or _ x < or _ 13)
Q3. It has been estimated that one in five Americans suffers from allergies. The president of Hargrove University plans to randomly select 10 students from the undergraduate population of 1400 to attend a dinner at his home. Assuming that Hargrove students are typical in terms of susceptibility to allergies and that the college president's home happens to contain just about every common allergen to which afflicted persons react, what is the probability that at least 8 of the students will be able to stay for the duration of the dinner event?
Q4. According to the Mortgage Bankers Association of America, the foreclosure rate on home mortgages in 2001 was 1%. Assuming that this rate is applicable to a community where 1000 homes have mortgages, use the Poisson approximation to the binomial distribution to determine the following for x = the number of foreclosures in this community during the coming year:
a. E(x)
b. P( x = 7)
c. P( x = 10)
d. P( 8