Question

If ?x is a binomial random variable, compute ?(?) for each of the following cases:

(a)  ?(?≤6),?=8,?=0.2

?(?)=

(b)  ?(?>4),?=5,?=0.5

?(?)=

(c)  ?(?<2),?=3,?=0.8

?(?)=

(d)  ?(?≥5),?=9,?=0.6

?(?)=

Answer 1

Solution:

Here, we have to find the probabilities by using the binomial table.

(a)  ?(?≤6),?=8,?=0.2

?(?≤6) = 0.999916

[By using cumulative binomial table.]

(b)  ?(?>4),?=5,?=0.5

?(?>4) = 1 - P(X≤4)

?(?>4) = 1 - 0.96875

[By using cumulative binomial table.]

?(?>4) = 0.03125

(c)  ?(?<2),?=3,?=0.8

?(?<2) = P(X≤1)

?(?<2) = 0.104

[By using cumulative binomial table.]

(d)  ?(?≥5),?=9,?=0.6

?(?≥5) = 1 - P(X<5)

?(?≥5) = 1 - P(X≤4)

?(?≥5) = 1 - 0.266568

[By using cumulative binomial table.]

?(?≥5) = 0.733432