1) An investor has two investments A and B. The investor believes that investment A is equally likely to increase by $1,000 or to decrease by $1,000 by the end of the year. The investor also believes that investment B is equally likely to increase by $2,000 or decrease by $2,000 by the end of the year. Let X represents the total amount of change in investments A and B. Assume that these investments perform independent of each other. Find the probability of X.
2) A random variable has possible values of 20, 21, 22, 23, and 24 that are equally likely to occur.
- What is the probability that the random variable is less than 23?
- What is the mean of the random variable?
- What is the standard deviation of the random variable?
3) Mergers and slow periods in the economy often result in layoffs at many firms. Many employees count on two or three months of severance pay to carry them over to the next job. However, job searches can sometimes take longer than 6 months. A survey of workers who have been with firms’ for more than a year revealed that only 30% of the workers would be financially secure if they lost their jobs for 6 months to a year. Let X represent the number of employees out of a sample of 80 who would feel financially secure if they lost their job for 6 months to a year.
- What is the probability that at least 30 employees out of 80 would be financially secure if they lost their job for 6 months to a year?
- Do a ‘what-if’ analysis by changing the probability to .4, and .5, and rework part a).
4) The vice president of a bank wishes to provide banking services so that the probability of the number of waiting customers being greater than 8 is less than .07. Would this condition be satisfied if the number of waiting customers is a Poisson random variable with a mean of 5? Justify your answer with appropriate calculations.