Statistics and Probability Answers

During summer vacations Tanuja wants to visit three cities, Kolkata, Bhubneshvar and Chennai
randomly .find the probability that she will visit ,1)Bhubneshvar before Chennai
2)Bhubneshvar just before Kolkata

Suppose a gene in a chromosome is of type A or type B. Assume that the probability that a gene of type A will mutate of type B in one generation is 10^−4 and that a gene of type B will mutate to type A is 10^−6.

(A) What is the transition matrix?
(B) After many generations, what is the probability that the gene will be of type A? or type B? (Find the stationary matrix.)

Test scores of ten individuals before and after a training program are shown below.

Individual - Score After Program - Score Before Program
1 - 57 - 59
2 - 62 - 57
3 - 60 - 60
4 - 63 - 66
5 - 69 - 68
6 - 63 - 59
7 - 74 - 72
8 - 56 - 52
9 - 64 - 58
10 - 64 - 63

What is the sum of positive signed ranks (T+)?

The mean µT is?

The value of σT is?

At α = 0.05, what can be concluded about the effectiveness of the training program?

At α = 0.2, what can be concluded about the effectiveness of the training program?

Student enrolment at a university over the past six years is given below.

Year (t) Enrolment (in 1000s)
1 6.3
2 7.7
3 8
4 8.2
5 8.8
6 8.0

a.What is the linear trend expression for the above time series?
b.Based on the model you determined in the question above, what is the forecast enrollment for year 10?

Consider the following annual series on the number of people assisted by a county’s human resources department.

Year: People:
1 22
2 24
3 28
4 24
5 22
6 24
7 20
8 26
9 24
10 28
11 26

a. What is the 3-year moving average for period 4?
b. What is the 3-year moving average forecast for period 12?
c. What is the Mean Square Error (MSE) for the 3-year moving average?
d. Using a smoothing constant of 0.4, what is the exponential smoothing value to be used as forecasts for period 4?
e. Using a smoothing constant of 0.4, what is the exponential smoothing value to be used as forecasts for period 12?
f. Using a smoothing constant of 0.4, what is the Mean Square Error (MSE) for exponential smoothing?

g. When comparing the accuracy of both forecasting techniques (3-year moving average and exponential smoothing with a 0.4 smoothing constant) we can conclude that

a golf ball is selected at random from a golf bag. IF the golf bag contains 8 brown balls, 9 black balls, and 3 red balls, find the probability that the golf ball is brown or black is

Provided below is a partial computer output based on a sample of 12 observations relating the number of personal computers sold by a computer shop per month (Y), unit price (X1 in $1,000) and the number of advertising spots (X2) they used on a local television station.

ANOVA Table
DF SS MS F Significance F
Regression 2 655.955
Error 9 182.96
Total 838.917

At α = 0.05 level of significance, what is the F value?

At α = 0.05 level of significance, what is critical F?

At α = 0.05 level of significance, is the regression model significant?

What is the multiple coefficient of determination?

What is the adjusted multiple coefficient of determination?

The table below shows the results of a study on smoking and three illnesses. We are interested in determining if the proportions of smokers in the three categories are different from each other.

Emphysema- Heart Problem- Cancer- Total
Smoker 145 140 300 585
Non-smoker 60 100 230 390
Total 205 240 530 975

p1 = proportions of smokers with emphysema

p2 = proportions of smokers with heart problem

p3 = proportions of smokers with cancer

a. What represents the null and alternative hypotheses in this case?

b. The expected frequency of smokers with emphysema is?

c. The chi-square value is?

d. With α = 0.1, the critical X2 value is?

e. P1 – P2 is? P2 - P3 is?

f. Using α = 0.1, the conclusion of the pairwise comparison is?

Write the t distribution and its properties with useful examples.

A hash table has space for 75 records, then the probability of collision before the table is 6% full.