Question

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?

Answer 1

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

$P(X=x)=0.3(1-0.3)^{x-1} , x=1,2,3...$

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

P(X=1) or P(X=2)=$0.3(1-0.3)^{1-1}+0.3(1-0.3)^{2-1}=0.51$

E)

$P(X \geq 3)=1-P(X$

F)

$E(X)=\frac{1}{p}$

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

p = 1-0.3 = 0.7

$E(X)=\frac{1}{0.7}=1.42$

G)$E(X)=\frac{1}{q}=\frac{1}{0.3}=3.33$