8/18/2019 Probability Final Paper

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Nepathya CollegeFinal Internal Exam

2072Bachelor Level/First Semester Full ar!s" #0S$%$& '0( )ass ar!s" 2*)ro+a+ility an, statistics $ime" ( -ours

.roup % 2'01201. There are three traffic lights on your way home. As you arrive at each light

assume that it is either red ( R ) or green (G) and that it is green with probability0.. !onstruct the sample space by listing all possible eight sample events. Assign probability to each sample event. Are the events e"ually li#ely$ %hat isthe probability that you stop no more than one time.

&. 'istinguish between correlation and regression. The city council of athmanduhas gathered data on number of minor accidents() and the number of youthfootball games(*) that occurred in town over the wee#ends.

* &0 +0 10 1& 1, &, +-

/ - , /

i) 'evelop the regression e"uation to predict minor accidents from football games.ii) !alculate standard error and coefficient of determination interpret the results.iii) !alculate /, confidence limits for population slope.

 

.roup B %ny eight 341 *0+. 2tate and prove 3aye4s theorem.-. %hat is a5iomatic definition of probability and what are its properties.,. The random variable * has the probability distribution shown below.

* 0 1 &

6(*75) 0.& 0.+ 0.,

a) 8ind 9(*) and :(*) b) !alculate 9() 7 +*;&. ointly distributed random variable with probability density function

given by f(5=y) 7#5y ? 0 5 y = 0 y@1 8ind˂ ˂ ˂i) constant # ii) marginal pdf of * and .

. 6rove that :(*;)7 :(*);:();&!:(*=). %rite the density function of negative e5ponential distribution and derive its mean

and variance.

/. 'efine canonical definition of chiB s"uare distribution. 'iscuss some of itsproperties and uses.

10. The systolic blood pressure of &0 years old women (*) is normally distributedwith mean 1&0mmCg and a standard deviation of 11&mmCg randomly selected&0 years old women. !ompute the following probabilities.

i)6(* 1,0)˃ ii) 6(* 11,)˂ iii) 6(11,@ *@ 1+0)11. 'efine 3inomial distribution. Ds there any consistency in the statement that the

mean of binomial distribution is &0 standard deviation is -. Df no inconsistency isfound what is the values of p= " and n.

Nepathya CollegeFinal Internal Exam

2072Bachelor Level/First Semester Full ar!s" #0S$%$& '0( )ass ar!s" 2*)ro+a+ility an, statistics $ime" ( -ours

.roup % 2'01201. There are three traffic lights on your way home. As you arrive at each light

assume that it is either red ( R ) or green (G) and that it is green with probability0.. !onstruct the sample space by listing all possible eight sample events. Assign probability to each sample event. Are the events e"ually li#ely$ %hat isthe probability that you stop no more than one time.

&. 'istinguish between correlation and regression. The city council of athmanduhas gathered data on number of minor accidents() and the number of youthfootball games(*) that occurred in town over the wee#ends.

* &0 +0 10 1& 1, &, +-

/ - , /

i) 'evelop the regression e"uation to predict minor accidents from football games.ii) !alculate standard error and coefficient of determination interpret the results.iii) !alculate /, confidence limits for population slope.

 

.roup B %ny eight 341 *0+. 2tate and prove 3aye4s theorem.-. %hat is a5iomatic definition of probability and what are its properties.,. The random variable * has the probability distribution shown below.

* 0 1 &

6(*75) 0.& 0.+ 0.,

a) 8ind 9(*) and :(*) b) !alculate 9() 7 +*;&. ointly distributed random variable with probability density function

given by f(5=y) 7#5y ? 0 5 y = 0 y@1 8ind˂ ˂ ˂i) constant # ii) marginal pdf of * and .

. 6rove that :(*;)7 :(*);:();&!:(*=). %rite the density function of negative e5ponential distribution and derive its mean

and variance.

/. 'efine canonical definition of chiB s"uare distribution. 'iscuss some of itsproperties and uses.

10. The systolic blood pressure of &0 years old women (*) is normally distributedwith mean 1&0mmCg and a standard deviation of 11&mmCg randomly selected&0 years old women. !ompute the following probabilities.

i)6(* 1,0)˃ ii) 6(* 11,)˂ iii) 6(11,@ *@ 1+0)11. 'efine 3inomial distribution. Ds there any consistency in the statement that the

mean of binomial distribution is &0 standard deviation is -. Df no inconsistency isfound what is the values of p= " and n.