Advertisements
Advertisements
प्रश्न
If X ~ B(n, p) such that 4P(X = 4) = P(x = 2) and n = 6. Find the distribution, mean and standard deviation of X
उत्तर
X ~ B(n, p)
Given, 4P(X = 4) = P(X = 2), n = 6
P(X = x) = ⁿCx px qn-x, x = 0, 1, 2, …. n
⇒ 4 6C4 p4 q2 = 6C2 p2 q4
⇒ 4p2 = q2
4(1 – q)2 = q2
4(1 – 2q + q2) = q2
3q2 – 8q + 4 = 0
(q – 2)(3q – 2) = 0
q = `2/3` (q ≠ 2)
Distribution
P(X = x) = `""^6"C"_x (1/3)^x (2/3)^(6-x)`
x = 0, 1, 2, 3, 4, 5, 6
Mean: = np
= `6 xx 1/3`
= 2
Variance: = npq
= `2 xx 2/3`
= `4/3`
APPEARS IN
संबंधित प्रश्न
Compute P(X = k) for the binomial distribution, B(n, p) where
n = 6, p = `1/3`, k = 3
Compute P(X = k) for the binomial distribution, B(n, p) where
n = 9, p = `1/2`, k = 7
The probability that Mr.Q hits a target at any trial is `1/4`. Suppose he tries at the target 10 times. Find the probability that he hits the target exactly 4 times
Using binomial distribution find the mean and variance of X for the following experiments.
A fair die is tossed 240 times and X denotes the number of times that four appeared
The probability that a certain kind of component will survive a electrical test is `3/4`. Find the probability that exactly 3 of the 5 components tested survive
A retailer purchases a certain kind of electronic device from a manufacturer. The manufacturer indicates that the defective rate of the device is 5%. The inspector of the retailer randomly picks 10 items from a shipment. What is the probability that there will be at least one defective item
If the probability that a fluorescent light has a useful life of at least 600 hours is 0.9, find the probabilities that among 12 such lights at least 11 will have a useful life of at least 600 hours
If the probability that a fluorescent light has a useful life of at least 600 hours is 0.9, find the probabilities that among 12 such lights at least 2 will not have a useful life of at least 600 hours
The mean and standard deviation of a binomial variate X are respectively 6 and 2. Find the probability mass function
The mean and standard deviation of a binomial variate X are respectively 6 and 2. Find P(X = 3)
The mean and standard deviation of a binomial variate X are respectively 6 and 2. Find P(X ≥ 2)
In a binomial distribution consisting of 5 independent trials, the probability of 1 and 2 successes are 0.4096 and 0.2048 respectively. Find the mean and variance of the random variable
Choose the correct alternative:
Let X have a Bernoulli distribution with a mean of 0.4, then the variance of (2X – 3) is
Choose the correct alternative:
If in 6 trials, X is a binomial variable which follows the relation 9P(X = 4) = P(X = 2), then the probability of success is
