It has been estimated that only about 30% of California residents have adequate earthquake supplies. Suppose we are interested in the number of California residents we must survey until we find a resident who does not have adequate earthquake supplies. a. In words, define the random variable X. b. List the values that Xmay take on. c. Give the distribution of X.X~ ___(_,___) d. WhatistheprobabilitythatwemustsurveyjustoneortworesidentsuntilwefindaCaliforniaresidentwhodoes not have adequate earthquake supplies? e. What is the probability that we must survey at least three California residents until we find a California resident who does not have adequate earthquake supplies? f. HowmanyCaliforniaresidentsdoyouexpecttoneedtosurveyuntilyoufindaCaliforniaresidentwhodoesnot have adequate earthquake supplies? g. How many California residents do you expect to need to survey until you find a California resident who does have adequate earthquake supplies?

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wifilethbridge wifilethbridge · Answer 1 · 2020-10-16T13:49:42+02:00

Answer:

Step-by-step explanation:

We are given that 30% of California residents have adequate earthquake supplies.

a) Ramon variable X denotes the number of the california residents that have adequate earthquake insurance

B) x can take value 1 ,2 ,3 ......

C)The distribution of random variable is geometric distribution with parameter p=0.3

The pmf of geometric distribution is

[tex]P(X=x)=0.3(1-0.3)^{x-1} , x=1,2,3...[/tex]

D)P(X=1) or P(X=2)=P(X=1)+P(X=2)

P(X=1) or P(X=2)=[tex]0.3(1-0.3)^{1-1}+0.3(1-0.3)^{2-1}=0.51[/tex]

E)

[tex]P(X \geq 3)=1-P(X<3)\\P(X \geq 3)=1-(P(X=1)+P(X=2))\\P(X \geq 3)=1-0.51\\P(X \geq 3)=0.49[/tex]

F)

[tex]E(X)=\frac{1}{p}[/tex]

p is the resident who does not have adequate earthquake supplies.

p = 1-0.3 = 0.7

[tex]E(X)=\frac{1}{0.7}=1.42[/tex]

G)[tex]E(X)=\frac{1}{q}=\frac{1}{0.3}=3.33[/tex]