Birla Institute of Technology (BIT Mesra) 2006 PROBABILITY & STATISTICS - Question Paper
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Birla Institute of Technology & Science, Pilani
Distance Learning Programmes Division
Second Semester 2006-2007
Mid-Semester Test
(EC-1 Regular)
Course No. : AAOC ZC111
Course Title : PROBABILITY & STATISTICS
No. of Pages = 1
No. of ques. = six
Nature of examination : Closed Book
Weightage : 40%
Duration : two Hours
Date of examination : 03/02/2007 (FN)
Note:
1. Please follow all the Instructions to Candidates provided on the cover page of the ans book.
2. All parts of a ques. should be answered consecutively. every ans should begin from a fresh page.
3. Mobile phones and computers of any type should not be brought inside the exam hall.
4. Use of any unfair means will outcome in severe disciplinary action.
Q.1. A bolt factory has 3 machines A, B and C that manufacture bolts 25, 35 and 40 percent respectively. Of the total of their output. 5, four and two percent bolts manufactured by machines A, B, and C respectively are defective. A bolt is drawn at random and is obtained to be defective. What is the probability that it was manufactured by machine B. (6)
Q.2. The probability of A will be residing for next ten years is 1/4 and that of B will be residing for next ten years is 1/3. obtain the probability that
a. Both will be residing for next ten years.
b. At lowest 1 of them will be residing for next ten years. (6)
Q.3. From a bag containing two 1 rupee- coins and three twenty paisa coins, a person is asked to draw 2 coins at random. obtain the value of his expectation. (6)
Q.4. obtain the mean and Variance of Poisson distribution. (8)
Q.5. The mean and variance of Binomial distribution are four and 4/3 respectively. obtain P(X = 1). (6)
Q.6. A random variable X has the subsequent probability distribution
x
0
1
2
3
4
5
6
7
P(x)
0
k
2k
2k
3k
k2
2k2
7k2+k
a. obtain k.
b. Evaluate P(X< 4), P(X = 4) and P(1
*****
| Earning: Approval pending. |
