Advertisements
Advertisements
प्रश्न
If X ~ B(n, p) with n = 10, p = 0.4, then find E(X2).
Advertisements
उत्तर
For X ~ B(n, p), E(X) = np and V(X) = npq
Given that n = 10 and p = 0.4
∴ q = 1 – p
= 1 – 0.4
= 0.6
∴ E(X) = np
= 10 × 0.4
= 4
and
V(X) = npq
= 10 × 0.4 × 0.6
= 2.4
Also, V(X) = E(X2) – [E(X)]2
∴ 2.4 = E(X2) – (4)2
∴ E(X2) = 2.4 + 16
∴ E(X2) = 18.4
APPEARS IN
संबंधित प्रश्न
A die is thrown 6 times. If ‘getting an odd number’ is a success, find the probability of 5 successes.
A die is thrown 6 times. If ‘getting an odd number’ is a success, find the probability of at least 5 successes.
A die is thrown 6 times. If ‘getting an odd number’ is a success, find the probability of at most 5 successes.
Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards, find the probability that only 3 cards are spades
Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards; find the probability that none is a spade.
In a box of floppy discs, it is known that 95% will work. A sample of three of the discs is selected at random. Find the probability that all 3 of the sample will work.
Choose the correct option from the given alternatives:
A die is thrown 100 times. If getting an even number is considered a success, then the standard deviation of the number of successes is ______.
Choose the correct option from the given alternatives:
The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is
Choose the correct option from the given alternatives:
For a binomial distribution, n = 5. If P(X = 4) = P(X = 3), then p = ______
For a binomial distribution, n = 4. If 2P(X = 3) = 3P(X = 2), then p = ______.
If X ~ B(4, p) and P(X = 0) = `16/81`, then P(X = 4) = ______.
Choose the correct option from the given alternatives:
The probability of a shooter hitting a target is `3/4` How many minimum numbers of times must he fire so that the probability of hitting the target at least once is more than 0·99?
If the mean and variance of a binomial distribution are 18 and 12 respectively, then n = ______.
Let X ~ B(10, 0.2). Find P(X = 1).
Let X ~ B(10, 0.2). Find P(X ≤ 8).
The probability that a bomb will hit a target is 0.8. Find the probability that out of 10 bombs dropped, exactly 2 will miss the target.
The probability that a mountain-bike travelling along a certain track will have a tyre burst is 0.05. Find the probability that among 17 riders: exactly one has a burst tyre
The probability that a mountain-bike travelling along a certain track will have a tyre burst is 0.05. Find the probability that among 17 riders: at most three have a burst tyre
The probability that a mountain-bike travelling along a certain track will have a tyre burst is 0.05. Find the probability that among 17 riders: two or more have burst tyre.
The probability that a lamp in a classroom will be burnt out is 0.3. Six such lamps are fitted in the class-room. If it is known that the classroom is unusable if the number of lamps burning in it is less than four, find the probability that the classroom cannot be used on a random occasion.
The probability that a machine will produce all bolts in a production run within specification is 0.998. A sample of 8 machines is taken at random. Calculate the probability that all 8 machines.
The probability that a machine will produce all bolts in a production run within specification is 0.998. A sample of 8 machines is taken at random. Calculate the probability that 7 or 8 machines.
The probability that a machine will produce all bolts in a production run within specification is 0.998. A sample of 8 machines is taken at random. Calculate the probability that at most 6 machines will produce all bolts within specification.
The probability that a machine develops a fault within the first 3 years of use is 0.003. If 40 machines are selected at random, calculate the probability that 38 or more will not develop any faults within the first 3 years of use.
A computer installation has 10 terminals. Independently, the probability that any one terminal will require attention during a week is 0.1. Find the probabilities that 3 or more, terminals will require attention during the next week.
In a large school, 80% of the pupil like Mathematics. A visitor to the school asks each of 4 pupils, chosen at random, whether they like Mathematics.
Calculate the probabilities of obtaining an answer yes from 0, 1, 2, 3, 4 of the pupils.
It is observed that it rains on 12 days out of 30 days. Find the probability that it rains exactly 3 days of week.
In binomial distribution with five Bernoulli’s trials, the probability of one and two success are 0.4096 and 0.2048 respectively. Find the probability of success.
If E(x) > Var(x) then X follows _______.
Fill in the blank :
In Binomial distribution probability of success Remains constant / independent from trial to trial.
In Binomial distribution if n is very large and probability success of p is very small such that np = m (constant) then _______ distribution is applied.
State whether the following statement is True or False:
For the Binomial distribution, Mean E(X) = m and Variance = Var(X) = m
If the sum of the mean and the variance of a binomial distribution for 5 trials Is 1.8, then p = ______.
If X follows a binomial distribution with parameters n = 10 and p. If 4P(X = 6) = P(X = 4), then p = ______
In a binomial distribution `B(n, p = 1/4)`, if the probability of at least one success is greater than or equal to `9/10`, then n is greater than ______.
In a binomial distribution, n = 4 and 2P(X = 3) = 3P(X = 2), then q = ______.
A pair of dice is thrown 3 times. If getting a doublet is considered a success, find the probability of getting at least two success.
Solution:
A pair of dice is thrown 3 times.
∴ n = 3
Let x = number of success (doublets)
p = probability of success (doublets)
∴ p = `square`, q = `square`
∴ x ∼ B (n, p)
P(x) = nCxpx qn–x
Probability of getting at least two success means x ≥ 2.
∴ P(x ≥ 2) = P(x = 2) + P(x = 3)
= `square` + `square`
= `2/27`
If X is a binomial variable with range {0, 1, 2, 3, 4} and P(X = 3) = 3P(X = 4) then the parameter ‘p’ of the binomial distribution is
