Statistics and Probability Answers

Let X, Y be a independent and identically distributed random variables, each having Poisson distribution with rate parameter λ. Find the probability generating function of W = X + Y and hence the mean and variance of W

The joint density function of the random variables X, Y is given as

f(x, y) = { 0.4 (2x + 3y), 0 < x < 1, 0 < y< 1

0, elsewhere

1)Determine P [ 0.33 < X < 2/3 |Y > 3 /4 ]

A dinner party is attended by five men and five women.

(a) How many unique ways can the 10 people sit around the table. (1)

(b) How many unique ways can the people sit around the table with men and women

alternating seats.

The examination results of a large group of students in Statistics are approximately normally distributed with a mean of 60 and a standard deviation of 9. If a student is chosen at random, what is the probability that his score is Below 45?

The average lifetime of 120 Brand X Alkaline AA batteries and 120 Brand Y alkaline AA batteries were found to be 9.1 hours and 9.6 hours respectively. Suppose the standard deviations of lifetimes are 1.9 for Brand X batteries and 2.1 hours for Brand Y batteries, test the hypothesis using α = 0.05

An aptitude test for selecting officers in a bank was conducted on 1,000 candidates, the average score is 42 and the standard deviation of scores is 24. Assume that the scores are normally distributed, answer the following questions.

i. What is the probability that the candidates score,

A.Exceed 65?

B.Between 40 and 60?

ii. Find the number of candidates whose score,

A. Exceed 40?

B. Lie between 40 and 65?

An aptitude test for selecting officers in a bank was conducted on 1,000 candidates, the average score is 42 and the standard deviation of scores is 24. Assume that the scores are normally distributed, answer the following questions.

i. What is the probability that the candidates score,

A. Exceed 65?

B. Between 40 and 60?

ii. Find the number of candidates whose score,

A. Exceed 40?

B. Lie between 40 and 65?