Advertisements
Advertisements
प्रश्न
An unbiased coin is tossed 4 times. Find the mean and variance of the number of heads obtained.
उत्तर
\[\text{ We have } , \]
\[p = \text{ probability of getting a head in a toss } = \frac{1}{2}, \]
\[q = \text{ probability of getting a tail in a toss } = \frac{1}{2}\]
\[\text{ Let X denote a success of getting a head in a toss . Then } , \]
\[\text{ X follows binomial distribution with parameters n = 4 and } p = \frac{1}{2}\]
\[ \therefore \text{ Mean } , E\left( X \right) = np = 4 \times \frac{1}{2} = 2\]
\[\text{ Also, variance, Var } \left( X \right) = npq = 4 \times \frac{1}{2} \times \frac{1}{2} = 1\]
APPEARS IN
संबंधित प्रश्न
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.
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?
Eight coins are thrown simultaneously. Find the chance of obtaining at least six heads.
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 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 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 all will graduate .
Suppose X has a binomial distribution with n = 6 and \[p = \frac{1}{2} .\] Show that X = 3 is the most likely outcome.
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 pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability distribution of the number of successes.
From a lot of 30 bulbs that includes 6 defective bulbs, a sample of 4 bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.
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
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.
The mean of a binomial distribution is 20 and the standard deviation 4. Calculate the parameters of the binomial distribution.
The probability that an item produced by a factory is defective is 0.02. A shipment of 10,000 items is sent to its warehouse. Find the expected number of defective items and the standard deviation.
The mean and variance of a binomial distribution are \[\frac{4}{3}\] and \[\frac{8}{9}\] respectively. Find P (X ≥ 1).
The mean of a binomial distribution is 10 and its standard deviation is 2; write the value of q.
If for a binomial distribution P (X = 1) = P (X = 2) = α, write P (X = 4) in terms of α.
If X follows a binomial distribution with parameters n = 100 and p = 1/3, then P (X = r) is maximum when r =
A fair die is tossed eight times. The probability that a third six is observed in the eighth throw 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 =
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
Find the mean and variance of the random variable X which denotes the number of doublets in four throws of a pair of dice.
For Bernoulli Distribution, state formula for E(X) and V(X).
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 ______.
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.
In three throws with a pair of dice find the chance of throwing doublets at least twice.
The mean and variance of binomial distribution are 4 and 2 respectively. Find the probability of two successes.
