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
The probability that a bomb will hit a target is 0.8. Find the probability that out of 10 bombs dropped, exactly 4 will hit the target.
There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?
Eight coins are thrown simultaneously. Find the chance of obtaining at least six heads.
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?
A bag contains 7 green, 4 white and 5 red balls. If four balls are drawn one by one with replacement, what is the probability that one is red?
A bag contains 2 white, 3 red and 4 blue balls. Two balls are drawn at random from the bag. If X denotes the number of white balls among the two balls drawn, describe the probability distribution of X.
A coin is tossed 5 times. If X is the number of heads observed, find the probability distribution of X.
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 .
Assume that the probability that a bomb dropped from an aeroplane will strike a certain target is 0.2. If 6 bombs are dropped, find the probability that exactly 2 will strike the target .
The probability that a student entering a university will graduate is 0.4. Find the probability that out of 3 students of the university none will graduate
Ten eggs are drawn successively, with replacement, from a lot containing 10% defective eggs. Find the probability that there is at least one defective egg.
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.
A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is \[\frac{1}{100} .\] What is the probability that he will win a prize exactly once.
How many times must a man toss a fair coin so that the probability of having at least one head is more than 90% ?
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 exactly two bulbs are defective
The mean of a binomial distribution is 20 and the standard deviation 4. Calculate the parameters of the binomial distribution.
If X follows a binomial distribution with mean 4 and variance 2, find P (X ≥ 5).
A die is tossed twice. A 'success' is getting an even number on a toss. Find the variance of number of successes.
The mean of a binomial distribution is 10 and its standard deviation is 2; write the value of q.
If X is a binomial variate with parameters n and p, where 0 < p < 1 such that \[\frac{P\left( X = r \right)}{P\left( X = n - r \right)}\text{ is } \] independent of n and r, then p equals
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 fair die is tossed eight times. The probability that a third six is observed in the eighth throw 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
A coin is tossed 4 times. The probability that at least one head turns up is
For a binomial variate X, if n = 3 and P (X = 1) = 8 P (X = 3), then p =
The probability of selecting a male or a female is same. If the probability that in an office of n persons (n − 1) males being selected is \[\frac{3}{2^{10}}\] , the value of n is
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 all are white ?
For Bernoulli Distribution, state formula for E(X) and V(X).
One of the condition of Bernoulli trials is that the trials are independent of each other.
Explain why the experiment of tossing a coin three times is said to have binomial distribution.
If x4 occurs in the tth term in the expansion of `(x^4 + 1/x^3)^15`, then the value oft is equal to:
If the coefficients of x7 and x8 in `(2 + x/3)^n` are equal, then n is
A box B1 contains 1 white ball and 3 red balls. Another box B2 contains 2 white balls and 3 red balls. If one ball is drawn at random from each of the boxes B1 and B2, then find the probability that the two balls drawn are of the same colour.
An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then the probability of getting an odd number for odd number of times is ______.
In three throws with a pair of dice find the chance of throwing doublets at least twice.
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.
