Download VNSGU MBBS First Year 2015 July M 4004 O Physiology Paper II Question Paper

II B.Tech I Semester Regular Examinations, November 2023

PROBABILITY AND STATISTICS

(CSE, IT)

Time: 3 hours Max. Marks: 70

Note: 1. Question paper consists of two parts A and B

2. Answer ALL the question in Part A

--- Content provided by‌ FirstRanker.com ---

3. Answer any FOUR questions from Part B

PART-A

1. a) Define Random variable. (2M)

b) Write properties of Binomial Distribution. (2M)

c) Define Null and Alternative hypothesis. (2M)

d) Write properties of t-distribution. (2M)

--- Content provided by⁠ FirstRanker.com ---

e) What is queuing theory? (2M)

f) Write about transient and steady state. (2M)

g) Define acceptance and rejection region. (2M)

PART-B

2. a) If the probability density of a random variable is given by $$ f(x)=\left\{\begin{array}{cc} k x^{2}, & -1

b) Out of 800 families with 5 children each, how many would you expect to have (7M)
i) 3 boys ii) atleast one boy iii) no girl iv) two or three girls

--- Content provided by FirstRanker.com ---

3. a) A normal population has a mean of 6.8 and S.D of 1.5. 54 samples of 40 are taken.(7M) Find the number of samples with means between 6.6 and 7.0.

b) A sales tax officer has imposed tax on 64 items and has obtained a mean of 480 with(7M) standard deviation of 100. Find 95% confidence interval for the mean.

4. a) Explain Type-I and Type-II errors. (7M)

b) A sample of 26 bulbs gives a mean life of 990 hours with a S.D of 20 hours. The(7M) manufacturer claims that the average life of bulbs is 1000 hours. Is the sample is not up to the standard.

5. a) Explain about ANOVA one-way classification. (7M)

--- Content provided by⁠ FirstRanker.com ---

b) The following data gives the number of aircraft accidents that occurred during the(7M) various days of the week. Test whether the accidents are uniformly distributed over the week.

6. a) Derive the differential equations of M/M/1 queuing system. (7M)

b) A telephone exchange has two long-distance operators. The telephone company finds(7M) that during the peak load long distance calls arrive in a Poisson fashion at an average rate of 15 per hour. The length of service on these calls is approximately exponentially distributed with mean length 5 minutes.
i) What is the probability that a subscriber will have to wait for his long distance call?
ii) What is the average waiting time in the queue?

--- Content provided by‌ FirstRanker.com ---

7. a) What are the characteristics of queuing system. (7M)

b) A super market has two girls serving at the counters. The customers arrive in Poisson(7M) fashion at the rate of 12 per hour. Each girl takes 6 minutes to serve a customer on average. Find
i) What is the probability that a customer has to wait for service?
ii) What is the expected percentage of idle time for each girl?

FirstRanker.com

--- Content provided by FirstRanker.com ---