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
Advertisements
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
The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. What is the probability that out of 5 such bulbs
(i) none
(ii) not more than one
(iii) more than one
(iv) at least one, will fuse after 150 days of use.
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)
A couple has two children, Find the probability that both children are females, if it is known that the elder child is a female.
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?
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 7 red, 5 white and 8 black balls. If four balls are drawn one by one with replacement, what is the probability that none is white ?
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?
The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs none will fuse after 150 days of use
Find the probability distribution of the number of sixes in three tosses of a die.
Five dice are thrown simultaneously. If the occurrence of 3, 4 or 5 in a single die is considered a success, find the probability of at least 3 successes.
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?
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 at least 2 will strike the target
An experiment succeeds twice as often as it fails. Find the probability that in the next 6 trials there will be at least 4 successes.
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 `1/100` What is the probability that he will win a prize at least twice.
How many times must a man toss a fair coin so that the probability of having at least one head is more than 80% ?
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
Determine the binomial distribution whose mean is 9 and variance 9/4.
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.
The mean of a binomial distribution is 20 and the standard deviation 4. Calculate the parameters of the binomial 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.
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.
In a binomial distribution, if n = 20 and q = 0.75, then write its mean.
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 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.
If X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9P(X = 3), then find the value of p.
If X follows a binomial distribution with parameters n = 8 and p = 1/2, then P (|X − 4| ≤ 2) equals
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 coin is tossed 10 times. The probability of getting exactly six heads 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
Mark the correct alternative in the following question:
A box contains 100 pens of which 10 are defective. What is the probability that out of a sample of 5 pens drawn one by one with replacement at most one is defective?
Mark the correct alternative in the following question:
The probability of guessing correctly at least 8 out of 10 answers of a true false type examination is
The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs not more than one will fuse after 150 days of use
Which one is not a requirement of a binomial distribution?
A pair of dice is thrown four times. If getting a doublet is considered a success then find the probability of two success.
If a random variable X follows the Binomial distribution B (33, p) such that 3P(X = 0) = P(X = 1), then the value of `(P(X = 15))/(P(X = 18)) - (P(X = 16))/(P(X = 17))` 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 student is given a quiz with 10 true or false questions and he answers by sheer guessing. If X is the number of questions answered correctly write the p.m.f. of X. If the student passes the quiz by getting 7 or more correct answers what is the probability that the student passes the quiz?
A fair coin is tossed 6 times. Find the probability of getting heads 4 times.
For the binomial distribution X ∼ B(n, p), n = 6 and P(X = 4) = P(X = 2). find p.
