Home
Class 12
MATHS
Suppose X has a binomial distribution B(...

Suppose X has a binomial distribution `B(6,1/2)`. Show that `X = 3`is the most likely outcome.(Hint: `P(x=3)`is the maximum among all `P(x_i),x_i=0,1,2,3,4,5,6)`

Text Solution

Verified by Experts

In a binomial distribution `B(6,1/2)`,
`n = 6 and p = 1/2`
Here, `n` is number of the trials and `p` is the success probability of each trial.
`:. q = 1- 1/2 = 1/2.`
Now, `P(X = k) = C(6,k) (1/2)^k(1/2)^(6-k) = (1/2)^6 C(6,k)`
So, most likely outcome will have maximum value of `C(6,k)`.
When `k = 0, C(6,0) = 1`
When `k = 1, C(6,1) = 6`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

(a) Obtain binomial probability distribution, if : (i) n=6,p=(1)/(3) (ii) n=5,p=(1)/(6) . (b) Suppose X has a binomial distribution B(6,(1)/(2)) . Show that X = 3 is the most likely outcome.

If for a binomial distribution P(X=1)=P(X=2)=alpha, write P(X=4) in terms of alpha.

In a binomial distribution with n= 4 2. P(X=3) =3. P (X=2) ,then the vlaue of p is

If for a binomial distribution with n=5, 4P(X=1)=P(X=2) , the probability of success is

If X has a poisson distribution such that P(x=2)=(2)/(3)P(x=1) then P(x=3) is

If X has a binomial distribution, B(n, p) with parameters n and p such that P(X = 2) = P(X = 3), then E(X), the mean of variable X, is

If X has a Poisson distribution such that P(x=2)=2/3 P(x=1) then find the value of P(x=3)

If X follows Binomial distribution with parameters n=5, p and P(X=2)=9P(X=3), then p is equal to ……. .

If X follows a binomial distribution with parameters n=6 and p. If 4(P(X=4))=P(X=2) , then P=

If X follows a binomial distribution with mean 3 and variance (3//2) find (i) P(X ge 1) (ii) P(X le 5)