Advertisements
Advertisements
प्रश्न
Suppose X has a binomial distribution `B(6, 1/2)`. Show that X = 3 is the most likely outcome.
(Hint: P(X = 3) is the maximum among all P (xi), xi = 0, 1, 2, 3, 4, 5, 6)
उत्तर
X is the random variable whose binomial distribution is `B(6, 1/2)`..
Therefore, n = 6 and p = 1/2
The value of `""^6C_3` is maximum. Therefore, for x = 3, P(X = x) is maximum.
Thus, X = 3 is the most likely outcome.
APPEARS IN
संबंधित प्रश्न
Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that
- all the five cards are spades?
- only 3 cards are spades?
- none is a spade?
A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?
A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is 1/100. What is the probability that he will in a prize (a) at least once (b) exactly once (c) at least twice?
A couple has two children, Find the probability that both children are females, if it is known that the elder child is a female.
Suppose that 90% of people are right-handed. What is the probability that at most 6 of a random sample of 10 people are right-handed?
The probability of a man hitting a target is 1/4. If he fires 7 times, what is the probability of his hitting the target at least twice?
Assume that on an average one telephone number out of 15 called between 2 P.M. and 3 P.M. on week days is busy. What is the probability that if six randomly selected telephone numbers are called, at least 3 of them will be busy?
If getting 5 or 6 in a throw of an unbiased die is a success and the random variable X denotes the number of successes in six throws of the die, find P (X ≥ 4).
The mathematics department has 8 graduate assistants who are assigned to the same office. Each assistant is just as likely to study at home as in office. How many desks must there be in the office so that each assistant has a desk at least 90% of the time?
The probability that a certain kind of component will survive a given shock test is \[\frac{3}{4} .\] Find the probability that among 5 components tested exactly 2 will survive .
In a hospital, there are 20 kidney dialysis machines and the chance of any one of them to be out of service during a day is 0.02. Determine the probability that exactly 3 machines will be out of service on the same day.
The probability that a student entering a university will graduate is 0.4. Find the probability that out of 3 students of the university only one will graduate .
The probability that a student entering a university will graduate is 0.4. Find the probability that out of 3 students of the university all will graduate .
In a 20-question true-false examination, suppose a student tosses a fair coin to determine his answer to each question. For every head, he answers 'true' and for every tail, he answers 'false'. Find the probability that he answers at least 12 questions correctly.
Find the probability that in 10 throws of a fair die, a score which is a multiple of 3 will be obtained in at least 8 of the throws.
A factory produces bulbs. The probability that one bulb is defective is \[\frac{1}{50}\] and they are packed in boxes of 10. From a single box, find the probability that more than 8 bulbs work properly
A box has 20 pens of which 2 are defective. Calculate the probability that out of 5 pens drawn one by one with replacement, at most 2 are defective.
Can the mean of a binomial distribution be less than its variance?
In a binomial distribution the sum and product of the mean and the variance are \[\frac{25}{3}\] and \[\frac{50}{3}\]
respectively. Find the distribution.
If the probability of a defective bolt is 0.1, find the (i) mean and (ii) standard deviation for the distribution of bolts in a total of 400 bolts.
Find the binomial distribution whose mean is 5 and variance \[\frac{10}{3} .\]
If a random variable X follows a binomial distribution with mean 3 and variance 3/2, find P (X ≤ 5).
A fair coin is tossed 100 times. The probability of getting tails an odd number of times is
The least number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.8, is
If the mean and variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than 1 is
A biased coin with probability p, 0 < p < 1, of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even is 2/5, then p equals
A fair die is tossed eight times. The probability that a third six is observed in the eighth throw is
Fifteen coupons are numbered 1 to 15. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is 9 is
A five-digit number is written down at random. The probability that the number is divisible by 5, and no two consecutive digits are identical, is
Five cards are drawn successively with replacement from a well-shuffled pack of 52 cards. What is the probability that only 3 cards are spades ?
Five cards are drawn successively with replacement from a well-shuffled pack of 52 cards. What is the probability that none is a spade ?
A bag contains 7 red, 5 white and 8 black balls. If four balls are drawn one by one with replacement, what is the probability that any two are white ?
The mean and variance of a binomial distribution are α and `α/3` respectively. If P(X = 1) = `4/243`, then P(X = 4 or 5) is equal to ______.
A fair coin is tossed 8 times. Find the probability that it shows heads at most once.
If the sum of mean and variance of a binomial distribution is `25/9` for 5 trials, find p.
For the binomial distribution X ∼ B(n, p), n = 6 and P(X = 4) = P(X = 2). find p.
