MCA4020- PROBABILITY AND STATISTICS

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ASSIGNMENT

 

 

 

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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