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ASSIGNMENT
DRIVE FALL | 2013 |
PROGRAM | MCA |
SUBJECT CODE & NAME | MCA4020- PROBABILITY AND STATISTICS |
SEMESTER | 4 |
BK ID | B1779 |
CREDITS | 4 |
MARKS | 60 |
Note: Answer all questions. Kindly note that answers for 10 marks questions should be approximately of 400 words. Each question is followed by evaluation scheme.
Q.1 A box contains 20 fuses of which 5 are defective. If 2 fuses are chosen together at random, what is the probability that both the fuses are defective?
Ans : Let A be the event the first fuse is defective and B the event that the second fuse is defective and A∩B represents the event the first fuse is defective and the second fuse is defective.
We use the concept of conditional probability o solve it and it states that :
The probability of an event B occurring when it is known that some event A has occurred is called a
conditional probability and is denoted by P(B/A)
The conditional probability of B, given A, denoted by P(B/A) is defined by:
P(B/A) = P(A)
P(A!B) if P(A) > 0
we may also write
Q.2 A coin is tossed until ahead appears. What is the expectation of the number of tosses required?
Ans :
Probability that it’s 1 is 1/2
Probability that it’s 2 is 1/2 x 1/2
–the first 1/2 is the probability that the first toss was a tail, the 2nd is that the second toss is a head.
Probability that it’s 3 is 1/2 x 1/2 x 1/2
Q.3 Calculate simple and Weighted arithmetic mean price tonnes of coal purchase by an industry for the half year.
months | jan | feb | mar | apr | may | jun |
price | 42.50 | 51 | 50 | 52 | 44.25 | 54 |
purchase | 25 | 30 | 40 | 50 | 10 | 45 |
Ans : In order to find out weighted average price per ton , we have to use the tons purchased as weights .
Table to Calculate simple and Weighted arithmetic average :
Q. 4 If the probability that an individual suffers a bad reaction from injection of a given serum is 0.001, find the probability that out of 2000 individuals (a) exactly 3, (b) more than 2, individuals will suffer from a bad reaction.
Ans : Step 1: Formula for Poisson distribution :
P (X = x) = e-λ⋅λxx!
Step 2: Given n = 2,000, p = 0.001
Step 3: l = n p = 2,000 × 0.001 = 2
Step 4: Number of individuals who will suffer a bad reaction x = 3
Q. 5 Construct Fisher’s Ideal Index number from the following data showing that it satisfies time reversal and factor reversal tests.
commodities | price | quantity | Price | quantity |
1999 | 2000 | |||
A | 10 | 100 | 12 | 144 |
B | 15 | 75 | 20 | 120 |
C | 8 | 80 | 10 | 110 |
D | 20 | 60 | 25 | 50 |
E | 50 | 500 | 60 | 540 |
Ans : To calculate Fisher’s ideal index number we need to draw the table :
Q. 6.Explain about the sampling distributions of a static and its standard error.
Ans : Sampling distribution :
In statistics, a sampling distribution or finite-sample distribution is the probability distribution of a given statistic based on a random sample. Sampling distributions are important in statistics because they provide a major simplification on the route to statistical inference. More specifically, they allow analytical considerations to be based on the sampling distribution of a statistic, rather than on the joint probability distribution of all the individual sample values.
he sampling distribution of a statistic is the distribution of that statistic, considered as a random variable, when derived from a random sample of
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