For binomial distribution E(x) = 2, V(x) = 4/3. Find the value of n.(a) 3(b) 4(c) 5(d) 6
Question
For binomial distribution E(x) = 2, V(x) = 4/3. Find the value of n.
(a) 3
(b) 4
(c) 5
(d) 6
Solution
In a binomial distribution, the expected value E(x) is equal to np and the variance V(x) is equal to npq, where n is the number of trials, p is the probability of success, and q is the probability of failure (1-p).
Given E(x) = 2 and V(x) = 4/3, we can set up the following equations:
np = 2 npq = 4/3
We can solve the first equation for p:
p = 2/n
Substitute p into the second equation:
n(2/n)q = 4/3 2q = 4/3 q = 2/3
Substitute q back into the first equation:
n(2/n)(2/3) = 2 2(2/3) = 2 n = 3
So, the value of n is 3, which corresponds to option (a).
Similar Questions
if the sum of the mean and variance of binomial distribution of 5trails is 4.8 ,find the corresponding pmf of the distribution
If mean and standard deviation of a binomial distribution is 10 and 2respectively; q will be ___(a) 1(b) 0.8(c) 0.6(d) 0.4
If a random variable X is binomially distributed with parameters n=5, p=0.4, then the probability of three successes is:a.0.18b.0.23c.0.36d.0.68
Suppose X follows a binomial distribution with n=30 trials and p=0.5 probability of success . Find μₓ, the mean of X. Do not round your answer.2 points
f x is a binomial random variable with n=10 and p=0.8, what is the probability that x is equal to 4?Select one:a..0055.b..0063.c..124.d..232.e..994.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.