8/18/2019 Nepathya College

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Probability and statistics (STAT- 103)

  Attempt all Questions.

  Group A (210!20)

1. a) Explain, for what purpose Karl Pearson’s coefficient of correlation is used for statistical analysis?State its major properties.  !) "he city council of Po#hara has $athered data on num!er of minor accidents and the num!er of 

youth foot!all $ames that occurred in town o%er the wee#ends. &

'(foot!all $ames) * * 1* 1 1+l +

- (minor accidents) / + & 0 /

i) e%elop the re$ression e2uation to predict minor accidents from foot!all $ames. ii) Predict num!er 

of minor accidents that will occur at wee#ends durin$ which '3*.

iii) 4alculate the %alue of coefficient of determination and standard error of estimate.

. Explain 5aye’s theorem. 6n a !olt factory machines 7, 5 and 4 manufactures +8, +8, and *8

respecti%ely of total. 9f their output +8, 8, and 8 are defecti%e !olts. 7 !olt is drawn at random

from the product and is found to !e defecti%e. :hat is the pro!a!ility that it was manufactured !y

machines 7, 5 and 4?  Group " ( any S6' ) ;+3 *

. iscuss axiomatic definition of pro!a!ility. 7lso define conditional pro!a!ility.

. "he pro!a!ility that an inte$rated circuit chip will ha%e defecti%e etchin$ is *.1, the pro!a!ility that it

will ha%e a crac# defect is *./ and the pro!a!ility that it has !oth defects is *.*&. what is the

 pro!a!ility that a newly manufactured chip will ha%e i) either an etchin$ or crac# defect ii) neither 

etchin$ nor crac# defect.

+. efine random %aria!le and discuss its types. 7n importer is offered a shipment of machine tools for