Respuesta :
Remainder of question:
Find the probability distribution of x
Answer:
The random variable x is defined as: X = {0, 1, 2, 3, 4}
The probability distribution of X:
P(X = 0) = 0.656
P(X = 1) = 0.2916
P(X= 2) = 0.0486
P(X=3) = 0.0036
P(X = 4) = 0.0001
Step-by-step explanation:
Sample size, n = 4
Random variable, X = {0, 1, 2, 3, 4}
10% (0.1) of the homeowners are insured against earthquake, p = 0.1
Proportion of homeowners who are not insured against earthquake, q = 1 - 0.1
q = 0.9
Probability distribution of x,
[tex]P(X = r) = ^nC_r *p^r q^{n-r} \\\\P(X= 0) =(^4C_0 *p^1 q^4 )\\P(X=0) = (^4C_0 *0.1^0 0.9^4 ) = 0.656\\P(X= 1)= (^4C_1 *p^1 q^3 )\\P(X=1) = (^4C_1 *0.1^1 0.9^3 ) = 0.2916\\P(X= 2)=( ^4C_2 *p^2 q^2) \\P(X=2) = (^4C_2 *0.1^2 0.9^2 ) = 0.0486\\P(X= 3) = (^4C_3 *p^3 q^3) \\ P(X=3) = (^4C_3 *0.1^3 0.9^1 ) = 0.0036\\P(X= 4) = (^4C_4 *p^4 q^0 )\\ P(X=4) =(^4C_4 *0.1^4 0.9^0 ) = 0.0001[/tex]
