Question

In each part, assume the random variable ?X has a binomial distribution with the given parameters. Compute the probability of the event.

(a) ?=6,?=0.5
??(?=3)=

(b) ?=6,?=0.1
??(?=2)=

(c) ?=4,?=0.7
??(?=2)=

(d) ?=4,?=0.5
??(?=3)=

Answer 1

Given that  the random variable X has a binomial distribution, now the probability of binomial distribution is calculated as:

Where

thus

a) For n =6, p =0.5, P( ? = 3) is calculated as:

b) For n = 6, p = 0.1 thus P(X = 2) is calculated as:

(c) n=4, p = 0.7, P(?=2) is calculated as:

P(2) = 0.2646

(d) For n = 4, p=0.5, P(?=3) is calculated as:

P(X = 3) = 0.25