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.
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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.
| Number of Heads | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Number of Tosses | 15 | 35 | 90 | 40 | 20 |
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.
Write any 10 characteristics of normal distribution.
Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the expected value for the number of kings.
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.
Find the probability that a third child in a family is the family's second daughter, assuming the male and female are equally probable.
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