SAPTHAGIRI COLLEGE OF ENGINEERING, BENGALURU-560 057
(Affiliated to VTU, Belagavi & Approved by AICTE, New Delhi)
DEPARTMENT OF MATHEMATICS
ACADEMIC YEAR: 2023-24(ODD SEMESTER)
ASSIGNMENT
SUB:MATHEMATICS FOR CSE SUB CODE:BCS301
1. Define:i) Random Variable ii) Discrete Probability Distribution, with an example.
2. Find the mean and variance of Poisson distribution.
3. Find the mean and variance of Binomial distribution.
4. Out of 800 families with 5 children each, how many would you expect to have (i) 3 𝑏𝑜𝑦𝑠 (ii) At least one
boy (iii) At most two boys, assuming equal probabilities for boys and girls..
5. A gambler’s luck follows’ a pattern. If he wins a game the Probability of winning the next game is 0.6.
However, if he loses a game, the probability of losing the next game is 0.7. There is an even chance of the
gambler winning the first game. (i) What is the probability of he winning the second game? (ii) What is the
probability of he winning the third game? (iii) In the long run, how often he will win?
0 3/4 1/4
6. Find the unique fixed probability vector of 𝐴 = [1/2 1/2 0 ]
0 1 0
7. Define (i) Alternative hypothesis (ii) A statistic (iii) Level of significance and (iv) Two-tailed test (V)
Standard error.
8. A die was thrown 9000 times and a throw of 5 or 6 was obtained 3240 times. On the assumption of random
throwing, do the data indicate an unbiased die at 1% level of significance.?
9. State Central limit theorem. Use the theorem to evaluate [50 < 𝑋̅ < 56] where 𝑋̅ represents the mean of a
random sample of size 100 from an infinite population with mean 𝜇 = 53 and variance 𝜎 2 = 400
10. . A die was thrown 60 times and the following frequency distribution was observed:
Faces 1 2 3 4 5 6
Frequency 15 6 4 7 11 17
Test whether the die is unbiased at 5% significance level.
11. Three different kinds of food are tested on three groups of rats for 5 weeks. The objective is to check the
difference in mean weight (in grams) of the rats per week. Apply one-way ANOVA using a 0.05 significance
level to the following data:
Food 1 8 12 19 8 6 11
Food 2 4 5 4 6 9 7
Food 3 11 8 7 13 7 9
12. Set up ANOVA table for the following information relating to three drugs testing to judge the effectiveness
in reducing blood pressure for three different groups of people
Group of people Drug
X Y Z
A 14 10 11
15 9 11
B 12 7 10
11 8 11
C 10 11 8
11 11 7
Do the drugs act differently? Are the different groups of people affected differently? Is the
interaction term significant? Answer the above questions taking a significant level of 5%.
13. Define (i) Alternative hypothesis (ii) A statistic (iii) Level of significance and (iv) Two-tailed test.
14. Explain the following terms i. Standard error ii. Statistical hypothesis iii. Critical region of a
statistical test iv. Test of significance
15. The following data show the number of worms quarantined from the GI areas of four groups of
muskrats in a carbon tetrachloride anthelmintic study. Conduct a two-way ANOVA test.
I II III 1V
33 41 12 38
32 38 38 35
26 40 46 25
14 23 22 13
30 21 11 26
