Some parts of California are particularly earthquake-prone. Suppose that in one metropolitan area, 26% of all homeowners are insured against earthquake damage. Four homeowners are to be selected at 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 that has insurance and F one who does not. Then one possible outcome is SFSS, with probability (0.26) (0.74) (0.26)(0.26) and associated X value 3. There are 15 other outcomes.] (Round your answers to four decimal places.) p(x) + Probability 0.4 0.3 02 0 (b) Draw the corresponding probability histogram. Probability 04 0.3 02 01 0.0 0.1 00 2 3 4 0 1 2 3 1 Number with earthquake Insurance Number with earthquake Insurance (c) What is the most likely value for X? Probability 2 0.4 56₂ Number with earthquake insurance 03 02 0.1 0.0 Probability 0.4 LL 03 02 01 3 0.0 Number with earthquake insurance 4 (d) What is the probability that at least two of the four selected have earthquake insurance? (Round your answer to four decimal places.)

er Weapon Handgun Rifle Shotgun Unknown firearm Knives Hands, fists, etc. Other Probability 0.478 0.027 0.035 0.148 0.135 0.059 0.118 to 0 and less than or equal to 1, and the sum of the probabilities of all outcomes E 14 quiz

Q P.6: On its way, a car meets 4 traffic lights, and the probability that each of them will be red is 0.5. Let X be a discrete random variable equal to the number of traffic lights that were green when the car arrived. X may take the values of 0, 1, 2, 3, 4. (Assume traffic lights are independent.) What is the probability distribution of X? The probability distribution of X is 3 4 p(x) 0.5 0.25 0.125 0.0625 0.0625 The probability of distribution of X is 3 p(x) 0.5 0.5 0.25 0.125 The probability of distribution of X is 3 4 p(x) 0.5 0.25 0.5 0.25 0.125 The probability distribution of X is 1 3 4 p(x) | 0.5 || 0.5 || 0.5 | 0.5 || 0.5 The probability of distribution of X is 3 4 p(x) || 0.0625 0.0625 0.125 0.25 0.5

Nicole has purchased the life insurance policy for her fish for the price of $200 per year and Nicole will receive $4000 in case if her fish passes away. The insurance company estimated the probability of her fish passing away during the length of the policy to be 0.5%. Let XX  be the insurance company's profit. Answer the following questions: 1. Create the probability distribution table for XX :  XX  outcome profit xx ,$  P(X=x)P(X=x)    fish passes away       fish survives     2. Use the probability distribution table to find the following:  E[X]=μX=E[X]=μX= dollars. (Round the answer to 1 decimal place.)  SD[X]=σX=SD[X]=σX= dollars. (Round the answer to 1 decimal place.)

Megan has purchased the insurance policy from an insurance company to cover the value of hers new car in case if it gets totaled for the price of $1500 per year. Megan's car worth $20000 and the probability of her totaling the car during the length of the policy is estimated to be 0.4%. Let XX be the insurance company's profit. Answer the following questions: 1. Create the probability distribution table for XX :  XX  outcome profit xx ,$  P(X=x)P(X=x)    car is totaled       car is not totaled     2. Use the probability distribution table to find the following:  E[X]=μX=E[X]=μX= dollars. (Round the answer to 1 decimal place.)  SD[X]=σX=SD[X]=σX= dollars. (Round the answer to 1 decimal place.)

A psychologist determined that the number of sessions required to obtain the trust of a new patient is either 1, 2, or 3. Let x be a random variable indicating the number of sessions re- quired to gain the patient's trust. The following probability function has been proposed. f(x) = for x = 1, 2, or 3 6. Is this probability function valid? Explain. b. What is the probability that it takes exactly two sessions to gain the patient's trust? с. What is the probability that it takes at least two sessions to gain the patient's trust?