Advertisements
Advertisements
प्रश्न
For X ~ B(n, p) and P(X = x) = `""^8"C"_x(1/2)^x (1/2)^(8 - x)`, then state value of n and p
उत्तर
P(X = x) = `""^"n""C"_x"P"^x"q"^("n" - x)`
For X ~ B(n, p) and P(X = x) = `""^8"C"_x(1/2)^x (1/2)^(8 - x)`
Comparing with equation (i), we get
n = 8 and p = `1/2`
APPEARS IN
संबंधित प्रश्न
A fair coin is tossed 8 times. Find the probability that it shows heads at least once
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?
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?
In an examination, 20 questions of true-false type are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers ‘true’; if it falls tails, he answers ‘false’. Find the probability that he answers at least 12 questions correctly.
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)
In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is
(A) 10−1
(B) `(1/2)^5`
(C) `(9/10)^5`
(D) 9/10
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?
In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is 5/6 . What is the probability that he will knock down fewer than 2 hurdles?
How many times must a man toss a fair coin so that the probability of having at least one head is more than 90%?
A fair coin is tossed 9 times. Find the probability that it shows head exactly 5 times.
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?
A bag contains 10 balls, each marked with one of the digits from 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?
In a large bulk of items, 5 percent of the items are defective. What is the probability that a sample of 10 items will include not more than one defective item?
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.
An unbiased die is thrown twice. A success is getting a number greater than 4. Find the probability distribution of the number of successes.
A card is drawn and replaced in an ordinary pack of 52 cards. How many times must a card be drawn so that (i) there is at least an even chance of drawing a heart (ii) the probability of drawing a heart is greater than 3/4?
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?
An unbiased coin is tossed 8 times. Find, by using binomial distribution, the probability of getting at least 6 heads.
Six coins are tossed simultaneously. Find the probability of getting
(i) 3 heads
(ii) no heads
(iii) at least one head
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 at most 3 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 .
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.
Suppose X has a binomial distribution with n = 6 and \[p = \frac{1}{2} .\] Show that X = 3 is the most likely outcome.
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 win a prize at least once.
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.
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 at least twice.
The probability of a man hitting a target is 0.25. He shoots 7 times. What is the probability of his hitting at least twice?
If the mean and variance of a binomial distribution are respectively 9 and 6, find the distribution.
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.
Find the binomial distribution whose mean is 5 and variance \[\frac{10}{3} .\]
The mean and variance of a binomial variate with parameters n and p are 16 and 8, respectively. Find P (X = 0), P (X = 1) and P (X ≥ 2).
In eight throws of a die, 5 or 6 is considered a success. Find the mean number of successes and the standard deviation.
If the sum of the mean and variance of a binomial distribution for 6 trials is \[\frac{10}{3},\] find the distribution.
A die is tossed twice. A 'success' is getting an even number on a toss. Find the variance of number of successes.
In a binomial distribution, if n = 20 and q = 0.75, then write its mean.
If in a binomial distribution mean is 5 and variance is 4, write the number of trials.
In a group of 200 items, if the probability of getting a defective item is 0.2, write the mean of the distribution.
If the mean of a binomial distribution is 20 and its standard deviation is 4, find p.
The mean of a binomial distribution is 10 and its standard deviation is 2; write the value of q.
If the mean and variance of a random variable X with a binomial distribution are 4 and 2 respectively, find P (X = 1).
If the mean and variance of a binomial variate X are 2 and 1 respectively, find P (X > 1).
If in a binomial distribution n = 4 and P (X = 0) = \[\frac{16}{81}\] , find q.
If the mean and variance of a binomial distribution are 4 and 3, respectively, find the probability of no success.
If for a binomial distribution P (X = 1) = P (X = 2) = α, write P (X = 4) in terms of α.
A rifleman is firing at a distant target and has only 10% chance of hitting it. The least number of rounds he must fire in order to have more than 50% chance of hitting it at least once is
A fair coin is tossed 100 times. The probability of getting tails an odd number of times is
A fair die is thrown twenty times. The probability that on the tenth throw the fourth six appears is
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
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
If the mean and variance of a binomial distribution are 4 and 3, respectively, the probability of getting exactly six successes in this distribution is
In a binomial distribution, the probability of getting success is 1/4 and standard deviation is 3. Then, its mean is
For a binomial variate X, if n = 3 and P (X = 1) = 8 P (X = 3), then p =
Mark the correct alternative in the following question:
Suppose a random variable X follows the binomial distribution with parameters n and p, where 0 < p < 1. If \[\frac{P\left( X = r \right)}{P\left( X = n - r \right)}\] is independent of n and r, then p equals
Mark the correct alternative in the following question:
The probability that a person is not a swimmer is 0.3. The probability that out of 5 persons 4 are swimmers is
Determine the binomial distribution where mean is 9 and standard deviation is `3/2` Also, find the probability of obtaining at most one success.
Find the mean and variance of the random variable X which denotes the number of doublets in four throws of a pair of dice.
Bernoulli distribution is a particular case of binomial distribution if n = ______
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.
Suppose a random variable X follows the binomial distribution with parameters n and p, where 0 < p < 1. If P(x = r)/P(x = n – r) is independent of n and r, then p equals ______.
The sum of n terms of the series `1 + 2(1 + 1/n) + 3(1 + 1/n)^2 + ...` is
A pair of dice is thrown four times. If getting a doublet is considered a success then find the probability of two success.
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 ______.
The probability of hitting a target in any shot is 0.2. If 5 shots are fired, find the probability that the target will be hit at least twice.
A fair coin is tossed 6 times. Find the probability of getting heads 4 times.
The mean and variance of binomial distribution are 4 and 2 respectively. Find the probability of two successes.
