x is a binomial random variable. (Give your answers correct to three decimal pla

Question

x is a binomial random variable. (Give your answers correct to three decimal places.)

(a) Calculate the probability of x for:    n = 7,    x = 1,    p = 0.8
P(x) =  

(b) Calculate the probability of x for:    n = 8,    x = 0,    p = 0.85
P(x) =  

(c) Calculate the probability of x for:    n = 3,    x = 2,    p = 0.4
P(x) =  

(d) Calculate the probability of x for:    n = 7,    x = 3,    p = 0.6
P(x) =  

(e) Calculate the probability of x for:    n = 6,    x = 3,    p = 0.35
P(x) =  

(f) Calculate the probability of x for:    n = 9,    x = 3,    p = 0.5
P(x) =

Explanation / Answer

Binomial Distribution
PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
a.
P( X = 1 ) = ( 7 1 ) * ( 0.8^1) * ( 1 - 0.8 )^6
= 0.0004
b.
P( X = 0 ) = ( 8 0 ) * ( 0.85^0) * ( 1 - 0.85 )^8
= 0.000000256
c.
P( X = 2 ) = ( 3 2 ) * ( 0.4^2) * ( 1 - 0.4 )^1
= 0.288
d.
P( X = 3 ) = ( 7 3 ) * ( 0.6^3) * ( 1 - 0.6 )^4
= 0.193536

Related Questions

Navigate

• Browse (All)
• Browse X
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.