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.
(a) True – If A, B, and C are mutually exclusive and exhaustive, then (P(A) + P(B) + P(C) = 1). Equations involving probabilities like (P(A \cup B) = ________ _______ ______ _________ ______.
___ ____ ___ _____ _____ ______ ______ ________ ______ _____ __________ _________.
_____ __________ __________ _______ _______ ____ ________ __________ _______.
_________ _________ ____ _________ ___ ________ ______.
_______ __________ _____ ______ ____.
______ _________ _____ ______ _____ _____ __________ __________ ______ _______ ____ _______.
_________ ________ _______ ____ _____ __________ ____ ___.
_________ ________ _________ _______ __________ __________ _______ _____ ____ ___ _______.
____ __________ _____ _________ __________ __________ _________ ______ _______.
_______ _____ _________ ______ ______ _______ ________ _______ _________.
__________ ___ ___ ____ ______ ________ _________ ___ _____ _______ _____.
_____ ____ __________ _________ ________ __________ ____ ________ ______ ___.
____ ___ ____ ___ ___ ____ ______ ___ _________.
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Find the probability that a third child in a family is the family's second daughter, assuming the male and female are equally probable.
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.
Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the expected value for the number of kings.
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?
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.
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
Write any 10 characteristics of normal distribution.