Let {X i, i ≥ 1} be independent and identically distributed random variables with (X i= 1) = p = 1 - P(X i= 0), S n= X i. The distribution of S nis?
Binomial distribution with parameter n and p
Each \(X_i\) takes value 1 with probability \(p\) and 0 with probability \(1-p\), so \(X_i \sim \text{Bernoulli}(p)\).
The sum of \(n\) i.i.d. Bernoulli\((p)\) variables counts the number of successes in \(n\) independent trials, which by definition follows a Binomial distribution with parameters \(n\) and \(p\), i.e. \(S_n \sim B(n,p)\).
Similar Questions
If X has Binomial distribution with parameters n and p such that np =λ, then \(\mathop {\lim }\limits_{n \to \infty } b\left( {x,n,p} \right);x = 0,1,2,.....\) is equal to:
If the independent random variables X,Y are Binomially distributed with n = 3, p = \(\dfrac{1}{3}\) and n = 5, p = \(\dfrac{1}{3}\) respectively, then the probability of (X + Y ≥ 1) is:
A random variable X is binomially distributed with parameter n = 25 and p = 0.2. The skewness of the variable X is
Important Questions from Binomial Distribution
In a Binomial distribution, the mean is three times its variance. What is the probability of exactly 3 successes out of 5 trials?
If mean and variance of a Binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than 1 is
For Binomial distribution, n = 10 and p = 0.6, E(X 2) (second moment about origin) is:
Find out the fallacy if any in the statement:
“The mean and the variance of a binomial distribution is 16.2 and 29.4 respectively.”
If log e(x) is normally distributed with mean 1 and variance 4, then P(0.5 < x < 2) is:
(where the area between z = 0 and z = 0.25 is 0.0987 and the area between z = 0 and z = 0.5 is 0.1915)
