1) Some parts of California are particularly earthquake prone. Suppose that in one metropolitan area that 25% of all homeowners are insured against earthquake damage. Four homeowners are to be schooled are random. Let X denote the number among the four who have earthquake insurance. a) Find the probability distribution of X. Hint: Let S denote a homeowner who has insurance, and let F denote a homeowner that does not have health insurance. Then one possible outcome is SFFS. What is the probability of this outcome? What value of X does this outcome correspond to? b) Draw corresponding probability histogram. c) What is the most likely value of X?

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1) Some parts of California are particularly earthquake prone. Suppose that in one metropolitan area that
25% of all homeowners are insured against earthquake damage. Four homeowners are to be schooled are
random. Let X denote the number among the four who have earthquake insurance.
a) Find the probability distribution of X.
Hint: Let S denote a homeowner who has insurance, and let F denote a homeowner that does not have health
insurance. Then one possible outcome is SFFS. What is the probability of this outcome? What value of X
does this outcome correspond to?
b) Draw corresponding probability histogram.
c) What is the most likely value of X?
d) What is the probability that at least two of the four people selected have earthquake insurance?
e) Find the cdf of X, F(X), write out the entire CDF as a piecewise function, and graph the resulting
function.
f) Using the CDF, calculate the probability of sampling between 1-3 people that have earthquake insurance.
Transcribed Image Text:1) Some parts of California are particularly earthquake prone. Suppose that in one metropolitan area that 25% of all homeowners are insured against earthquake damage. Four homeowners are to be schooled are random. Let X denote the number among the four who have earthquake insurance. a) Find the probability distribution of X. Hint: Let S denote a homeowner who has insurance, and let F denote a homeowner that does not have health insurance. Then one possible outcome is SFFS. What is the probability of this outcome? What value of X does this outcome correspond to? b) Draw corresponding probability histogram. c) What is the most likely value of X? d) What is the probability that at least two of the four people selected have earthquake insurance? e) Find the cdf of X, F(X), write out the entire CDF as a piecewise function, and graph the resulting function. f) Using the CDF, calculate the probability of sampling between 1-3 people that have earthquake insurance.
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answere d,e,f

1) Some parts of California are particularly earthquake prone. Suppose that in one metropolitan area that
25% of all homeowners are insured against earthquake damage. Four homeowners are to be schooled are
random. Let X denote the number among the four who have earthquake insurance.
d) What is the probability that at least two of the four people selected have earthquake insurance?
e) Find the cdf of X, F(X), write out the entire CDF as a piecewise function, and graph the resulting
function.
f) Using the CDF, calculate the probability of sampling between 1-3 people that have earthquake insurance.
Transcribed Image Text:1) Some parts of California are particularly earthquake prone. Suppose that in one metropolitan area that 25% of all homeowners are insured against earthquake damage. Four homeowners are to be schooled are random. Let X denote the number among the four who have earthquake insurance. d) What is the probability that at least two of the four people selected have earthquake insurance? e) Find the cdf of X, F(X), write out the entire CDF as a piecewise function, and graph the resulting function. f) Using the CDF, calculate the probability of sampling between 1-3 people that have earthquake insurance.
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