IGNOU MST 3 SOLVED ASSIGNMENT

Ques 1.

State whether the following statements are True or False. Give a reason in support of your answer.

(a) If events A, B and C are three mutually exclusive and exhaustive events, then it is possible that ,  and .

(b) If X is a discrete random variable, then X cannot take countably infinite values.

(c) If X is a standard normal variate, then .

(d) If random variables X and Y follow Bernoulli distributions with parameters 1/2 and 1/3 respectively then the random variable X + Y also follows a Bernoulli distribution with parameter 5/6.

Ques 2.

If a problem is randomly selected from a particular book, then probability that students A, B and C can solve the problem are 1/2, 1/3 and 1/4 respectively. If a problem is selected randomly from this book and given to the students A, B and C then what is the probability that problem is solved. They solve the problem independently.

Ques 3.

A factory produces certain type of output by 3 machines. The respective daily production figures are- machine X : 4500 units, machine Y: 2000 units and machine Z: 3500 units. Past experience shows that 2% of the output produced by machine X is defective. The corresponding fractions of defectives for the other two machines are 5 and 10 percent respectively. An item is drawn from the day's production. If the drawn item is found to be defective, what is the probability that it has been produced by machine Y?

Ques 4.

Find the probability that a third child in a family is the family's second daughter, assuming the male and female are equally probable.

Ques 5.

Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the expected value for the number of kings.

Ques 6.

 Three unbiased coins are tossed simultaneously. In which of the following cases are the events A and B independent?

(i) A be the event of getting exactly one tail

B be the event of getting exactly one head

(ii) A be the event that first coin shows tail

B be the event that third coin shows head

Ques 7.

 Write any 10 characteristics of normal distribution.

Ques 8.

Four coins were tossed and number of heads noted. The experiment is repeated 200 times. The number of tosses showing 0, 1, 2, 3 and 4 heads were found distributed as under. Fit a binomial distribution to these observed results assuming that the nature of the coins is not known.

Ques 9.

State whether the following statements are True or False. Give a reason in support of your answer.

(a) If events A, B and C are three mutually exclusive and exhaustive events, then it is possible that ,  and .

(b) If X is a discrete random variable, then X cannot take countably infinite values.

(c) If X is a standard normal variate, then .

(d) If random variables X and Y follow Bernoulli distributions with parameters 1/2 and 1/3 respectively then the random variable X + Y also follows a Bernoulli distribution with parameter 5/6.

Ques 10.

If a problem is randomly selected from a particular book, then probability that students A, B and C can solve the problem are 1/2, 1/3 and 1/4 respectively. If a problem is selected randomly from this book and given to the students A, B and C then what is the probability that problem is solved. They solve the problem independently.

Ques 11.

A factory produces certain type of output by 3 machines. The respective daily production figures are- machine X : 4500 units, machine Y: 2000 units and machine Z: 3500 units. Past experience shows that 2% of the output produced by machine X is defective. The corresponding fractions of defectives for the other two machines are 5 and 10 percent respectively. An item is drawn from the day's production. If the drawn item is found to be defective, what is the probability that it has been produced by machine Y?

Ques 12.

Find the probability that a third child in a family is the family's second daughter, assuming the male and female are equally probable.

Ques 13.

Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the expected value for the number of kings.

Ques 14.

 Three unbiased coins are tossed simultaneously. In which of the following cases are the events A and B independent?

(i) A be the event of getting exactly one tail

B be the event of getting exactly one head

(ii) A be the event that first coin shows tail

B be the event that third coin shows head

Ques 15.

 Write any 10 characteristics of normal distribution.

Ques 16.

Four coins were tossed and number of heads noted. The experiment is repeated 200 times. The number of tosses showing 0, 1, 2, 3 and 4 heads were found distributed as under. Fit a binomial distribution to these observed results assuming that the nature of the coins is not known.

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