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- a. Which of the following CANNOT be a probability distribution? Explain.i. p(x) = x / 6 for x = 1,2,3ii. p x = x for x = 1,2,3iii. p(x) = x / 5 for x = 1,0,1 b. An investor has $1000 available for a 1-year investment. The investor isconsidering the following three options:Option APossible return 30% 20% 0% -20%Probability 25% 40% 20% 15%Option BPossible return 50% 30% 0% -40%Probability 15% 50% 20% 15%Option CGuaranteed return 10%Probability 100%i. Based on the expected returns, which of these options should theinvestor choose?ii. Compute the standard deviations for Option A and Option B. Whichone of options A, B, and C has the least risk (i.e. the smallest standarddeviation), which one has the highest risk? What can you say aboutthe relationship between the expected returns and the risks of financialassets in the normal situation?2. Graph each distribution using a probability histogram. a) P(x) b) P(x) 0.05 1 12 4 0.13 5 12 1 6. 0.24 8. 0.38 1 3 10 0.12 1 12 0.05 3 14 0.03Let X = {Email, In Person, Instant Message, Text Message}; P(Email) = 0.06 P(In Person) = 0.55 P(Instant Message) = 0.24 P(Text Message) = 0.15 Is this model a probability distribution? A. Yes. B. No. C. Maybe.
- 1. Which of the following is a probability distribution? a. x 3 6 12 15 b. x 2. 3. 5. P(x) -0.3 0.5 0.1 0.3 0.4 P(x) 1.2 1.1 1.4 1.1 1.1 C. X 2 3 4 5 d. x 1. 2. 4 5 P(x) .49 .05 32 .07 .07 P(x) -.02 0.5 0.6 0.1 1 4.In how many ways can all of the letters in the word ISOSCELES be arranged if the arrangement must: a) start with E and end with E b) Have S for the middle letter c) have the vowels togrther d) have the consonants together e) ha ve the consonants and vowels alternateconsider the following Probability Distribution for Sales table probability: .3 .24 .14 .21 .11 sales: 29 35 55 66 80 find E(x), variance and riskiness
- 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.)Solve the following problems. 1. A bakeshop owner determines the number of boxes of hopia that are delivered each day. Find the mean of the probability distribution shown. Number of Boxes (X) Probability P (X) 35 0.10 36 0.20 37 0.30 38 0.30 39 0.10 2. The probabilities that a surgeon operates on 3, 4, 5, 6, or 7 patients in any day are 0.10, 0.20, 0.15, 0.30 and 0.25, respectively. Find the mean of the probability distribution using the formula. 3. Suppose your wallet contains ten P20 bills, five P50 bills, three P100 bills, one P500 bill, and one P1000 bill. Find the u of this distribution and interpret the result.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.)
- 315. During a recent period of high unemployment, hundreds of thousands of drivers dropped their automobile insurance. Sample data representative of the national automobile insur- ance coverage for individuals 18 years of age and older are shown here. b. C. Age 18 to 34 35 and over 60 Automobile Insurance Yes 1500 1900 a. Develop a joint probability table for these data and use the table to answer the remaining questions. No 340 260 What do the marginal probabilities tell you about the age of the U.S. population? What is the probability that a randomly selected individual does not have automobile insurance coverage? d. If the individual is between the ages of 18 and 34, what is the probability that the individual does not have automobile insurance coverage? e. If the individual is age 35 or over, what is the probability that the individual does not have automobile insurance coverage? f. If the individual does not have automobile insurance, what is the probability that the individual is…A survey of almost 44,000 two-child families yielded the accompanying table. The probability distribution of x, the number of boys in a two-child family is given below. Find E(x) and give a practical interpretation of its value. Gender Configuration Proportion D Girl-girl (GG) Boy-girl (BG) Girl-Boy (GB) 0.215 0.267 0.256 P(x) 0.215 0.523 0.262 Boy-boy (BB) 0.262 Choose the correct answer below and fill in the answer box to complete your choice. (Round to three decimal places as needed.) O A. If a very large number of households were sampled, on average, there would be E(x) = boys. O B. If a very large number of two-child households were sampled, on average, there would be E(x) = boys. of getting a family with a boy. %3D O C. If a very large number of two-child households were sampled, there would be a probability of E(x) = O D. In the sample of 44,000 households, each household had E(x) = boys.
