Respuesta :
Answer:
a) 10 weeks
b) P(k≤2)=0.190
c) P(k>17)=0.167
Step-by-step explanation:
This problem can be solved applying the geometric distribution.
The probability of needing k weeks to find an acceptable apartment can be written as:
[tex]P(k)=(1-p)^{k-1}p=0.9^{k-1}\cdot 0.1[/tex]
a) The expected value of this distribution is:
[tex]E(x)=1/p=1/0.1=10[/tex]
Answer: 10 weeks
b) The probability of finding an acceptable department in the first 2 weeks is:
[tex]P(k\leq2)=P(1)+P(2)=0.1*0.9^0+0.1*0.9^1\\\\P(k\leq 2)=0.1+0.09=0.19[/tex]
c) We have to calculate P(k>17)
[tex]P(k>17)=1-\sum_1^{17}P(k_i)\\\\P(k>17)=1-(P(1)+P(2)+P(3)+...+P(17))\\\\P(k>17)=1-(0.1+0.09+0.081+0.073+0.066+0.059+0.053+0.048+0.043+0.039+0.035+0.031+0.028+0.025+0.023+0.021+0.019)\\\\P(k>17)=1-0.833=0.167[/tex]
