Question

 

Consider a binomial experiment with

n = 10

and

p = 0.40.

(a)

Compute

f(0).

(Round your answer to four decimal places.)

f(0) =

(b)

Compute

f(2).

(Round your answer to four decimal places.)

f(2) =

(c)

Compute

P(x ≤ 2).

(Round your answer to four decimal places.)

P(x ≤ 2) =

(d)

Compute

P(x ≥ 1).

(Round your answer to four decimal places.)

P(x ≥ 1) =

(e)

Compute

E(x).

E(x) =

(f)

Compute

Var(x)

and σ. (Round your answer for σ to two decimal places.)

Var(x)

=σ=

Answer 1

Solution:

X follows Binomial(n = 10 , p = 0.40)

The PMF of X is given by

P(X = x) = (_n C _x) * p^x * (1 - p)^{n - x} ; x = 0 ,1 , 2 , ....., n

Use Binomial table or calculator or excel

a)

f(0) = (₁₀ C ₀) * 0.40⁰ * (1 - 0.40)^{10 - 0} = 0.0060

f(0) = 0.0060

b)

f(2) = 0.1209

c)

P(x ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0060466176+0.040310784+0.120932352

P(x ≤ 2) = 0.1673

d)

P(x ≥ 1) = 1 - {P(X < 1)} = 1 - { P(X = 0)} = 1 - 0.0060466176 = 0.9940

P(x ≥ 1) = 0.9940

e)

E(x) = n * p = 10 * 0.40 = 4

E(x) = 4

Var(X) = n * p * ( 1 - p ) = 10 * 0.4 * (1 - 0.4) = 2.4

Var(X) = 2.4

σ = Variance = 2.4 = 1.55

σ = 1.55