Let X sim B(6, 1/2). Then the maximum probabi | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) For a binomial distribution $X \sim B(n, p)$, the probability mass function is given by $P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$.Here, $n = 6$ an

Vedclass · Accepted Answer

$X = 3$

Vedclass · Answer

(C) For a binomial distribution $X \sim B(n, p)$, the probability mass function is given by $P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$.Here, $n = 6$ and $p = 1/2$.Since $p = 1/2$, the distribution is symmetric.For a symmetric binomial distribution, the maximum probability occurs at the mean, which is $E[X] = np = 6 	imes (1/2) = 3$.Alternatively, calculating for $k=3$: $P(X=3) = \binom{6}{3} (1/2)^3 (1/2)^3 = 20 	imes (1/64) = 20/64$.For $k=2$ or $k=4$: $P(X=2) = P(X=4) = \binom{6}{2} (1/2)^6 = 15 	imes (1/64) = 15/64$.Since $20/64 > 15/64$, the maximum probability occurs at $X = 3$.

Let $X \sim B(6, 1/2)$. Then the maximum probability occurs at

Similar Questions

In a box containing $100$ bulbs,$10$ are defective. The probability that out of $20$ bulbs selected at random,none is defective is

If the mean and the variance of a Binomial variate $X$ are $2$ and $1$ respectively,then the probability that $X$ takes a value greater than $1$ is equal to

$A$ random variable $X \sim B(n, p)$. If the values of the mean and variance of $X$ are $18$ and $12$ respectively,then the total number of possible values of $X$ is:

The probability that an event will fail to happen is $0.05$. The probability that the event will take place on $4$ consecutive occasions is

Vedclass Test Series

Exam Paper Generator

Online Exam Module