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).

Question

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).

Knowee AI · Accepted Answer

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).

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.

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