Question

Provide P (X ≥ 2).  Let X be a random variable. The set of all the possible values that X takes is ={0,1,2,3}

Suppose X is a binomial random variable with success probability p = 0.6. Provide P (X ≥ 2).

Why n here is 3, not 4?

Answer 1

We are given that the possible values X can take are 0,1,2 and 3. Moreover, we are given that X is a binomial random variable with success probability p = 0.6. Thus, we can conclude that:

X ~ Binomial(n = 3, p = 0.6)

Here n = 3 and not 4 because the possible values a Binomial(n,p) random variable can take are {0,1,2,...,n}, i.e., the maximum value a Binomial(n,p) random variable can take is n. Here since, the possible values of X are {0,1,2,3}, i.e., the maximum possible value of X is 3, thus X follows a Binomial distribution with n = 3 and not 4. [ANSWER]

Now, the probability mass function of X is given by:

Now, the required probability is given by:

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