Advertisements
Advertisements
प्रश्न
For Bernoulli Distribution, state formula for E(X) and V(X).
Advertisements
उत्तर
Bernoulli distribution is a particular case of binomial distribution if n = 1.
In binomial distribution if X ~ B(n, p) then E(X) = np and V(X) = npq.
∴ For bernoulli distribution, we get
E(X) = p and V(X) = pq.
APPEARS IN
संबंधित प्रश्न
A fair coin is tossed 8 times. Find the probability that it shows heads at least once
A pair of dice is thrown 4 times. If getting a doublet is considered as success, find the probability of two successes.
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)
On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?
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?
It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles, 9 are defective?
A couple has two children, Find the probability that both children are males, if it is known that at least one of the children is male.
A couple has two children, Find the probability that both children are females, if it is known that the elder child is a female.
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?
Five cards are drawn successively with replacement from a well-shuffled pack of 52 cards. What is the probability that all the five cards are spades ?
Find the probability distribution of the number of doublets in 4 throws of a pair of dice.
Find the probability distribution of the number of sixes in three tosses of a die.
Three cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the mean and variance of number of red cards.
A man wins a rupee for head and loses a rupee for tail when a coin is tossed. Suppose that he tosses once and quits if he wins but tries once more if he loses on the first toss. Find the probability distribution of the number of rupees the man wins.
The items produced by a company contain 10% defective items. Show that the probability of getting 2 defective items in a sample of 8 items is
\[\frac{28 \times 9^6}{{10}^8} .\]
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?
Six coins are tossed simultaneously. Find the probability of getting
(i) 3 heads
(ii) no heads
(iii) at least one head
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 .
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
It is known that 60% of mice inoculated with a serum are protected from a certain disease. If 5 mice are inoculated, find the probability that none contract the disease .
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
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 .
Can the mean of a binomial distribution be less than its variance?
Determine the binomial distribution whose mean is 20 and variance 16.
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.
A die is thrown three times. Let X be 'the number of twos seen'. Find the expectation of X.
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.
If the mean and variance of a binomial variate X are 2 and 1 respectively, find P (X > 1).
If X follows binomial distribution with parameters n = 5, p and P(X = 2) = 9P(X = 3), then find the value of p.
A fair coin is tossed 100 times. The probability of getting tails an odd number of times 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
Let X denote the number of times heads occur in n tosses of a fair coin. If P (X = 4), P (X= 5) and P (X = 6) are in AP, the value of n is
A coin is tossed 10 times. The probability of getting exactly six heads is
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
One of the condition of Bernoulli trials is that the trials are independent of each other.
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
If a random variable X follows the Binomial distribution B(5, p) such that P(X = 0) = P(X = 1), then `(P(X = 2))/(P(X = 3))` is equal to ______.
A fair coin is tossed 8 times. Find the probability that it shows heads at most once.
A fair coin is tossed 6 times. Find the probability of getting heads 4 times.
If X ∼ B(n, p), n = 6 and 9 P(X = 4) = P(X = 2), then find the value of p.
An experiment succeeds thrice as often as it fails. Then in next five trials, find the probability that there will be two successes.
