Statistics and Probability Answers

If X & Y are symmetric random variables, then show that E(X/X+Y)= 1/2

Because of economic conditions, a firm reports that 30% of its accounts receivable from other business firm are overdue. If an accountant takes a random sample of five such accounts, determine the probability that at least two accounts is overdue.

The mean height of a class of 28 students is 162 cm. A new student of height 149 cm joins the class. What is the mean height of the class now?

How does a z Score differ from a t score?

Associated with a job are two random variables: CPU time required (Y) and number of disk I/O
Operations (X).
i Time
(sec)
yi Number
xi
1 40 398
2 38 390
3 42 410
4 50 502
5 60 590
6 30 305
7 20 210
8 25 252
9 40 398
10 39 392

(i) Find the regression equation.
(ii) What is the estimate increase in CPU time for one additional disk operation.
(iii) Comment on the goodness of the model.

(i) Each computer chip made in a certain plant will, independently, be defective with probability 0.25. If a sample of 1,000 chips is tested, what is the approximate probability that fewer than 200 chips will be defective?
(ii) A manufacturer of computer terminals claims that its product will last at least for 500 hours without needing repairs. Soft-i-Tech is considering buying many computer terminals. But, it wants to ensure that the claim made by the manufacturer is reasonably true.
Soft-i-Tech’s quality control managers examine the records of the manufacturer and find that a sample of 100 terminals had the average time before first breakdown occurred was 48 hours with a sample standard deviation of 25 hours.
Use this scenario that as you decrease α, say from 0.5 to 0.1 β(49) increases. What is the conclusion from this?

If the moment generating function of X is given by , find c such that
(i) P[|X|<=c] =0.95. (ii) P[X>=c] = 0.025 (iii) P[X>c] = 0.5

A consumer buys n light bulbs, each of which has a life time that has a mean of 800 hours and a standard deviation of 100 hours. A light bulb is replaced by another as soon as it burns out. Assuming independence of life times, find the smallest value of n so that the succession of light bulbs produces light bulbs for at least 10,000 hours with a probability of 0.9. Do you think it is necessary to know the probability distribution of the light bulbs? Explain.

Consider the test H0: μ <=100 vs H1: μ >100 Suppose that a sample of size 36 has a sample mean of 105. (i) Determine the p-value of this outcome if the population standard deviation is known to be 15. (ii) Based on the p-value obtained in (i) above for what values of α you would Reject H0 (a) 0.01, (b) 0.02 (c) 0.06. You are not expected to perform the test all over again for each value of α; instead conclude based on outcome of (i) above.

A test consists of 70 multiple choice questions, each with five possible answers, only one of which is
correct. Find the mean and the standard deviation of the number of correct answers.