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- A part-time employee works for 1, 2 or 3 hours per day, each with a probability of 1/3. The number of hours worked on each day is also independent of the hours on any other day. Suppose the hourly rate is $10. Let his/her total salary for a two-day period be ?. Find the expected value and variance of ?.You sample a random observation of a Poisson distributed random variable with expected value 1. The result of the random draw determines the number of times you toss a fair coin. What is the probability distribution of the number of heads you will obtain?According to a survey, 30% of college students said that they spend too much time on Facebook. Suppose this result holds true for the current population of all college students. A random sample of six college students is selected. a. Define the random variable X b. X takes on what values?X = ..................................................... c. Determine the number of trials n and the probability of success for this binomial distribution. d.Find the probability that exactly three of these six college students will say that they will spend too much time on Facebook. Round your answer to three decimal places.
- For a particular population, a sample of n = 4 scores has an expected value of 10. For the same population, a sample of n = 25 scores would have an expected value of _____.A diagnostic test for disease X correctly identifies the disease 88% of the time. False positives occur 11%. It is estimated that 2.78% of the population suffers from disease X. Suppose the test is applied to a random individual from the population. Compute the following probabilities. The percentage chance that, given a negative result, the person does not have disease X= The percentage chance that, the person will be misclassified =Kindey failure is due to either natural occurrences (80%) or outside factors (20%). Outside factors are related to induced substances or foreign objects. Natural occurrences are caused by disease, and infection. Assume that causes of kidney failure for the individuals are independent. What is the probability that the third patient with kidney failure who enters the emergency room is the second patient due to outside factors? Let X denote a negative binomial random variable. (Show solutions) a. NONE O b.0.008 Oc.0.064 O d.0.256
- 3. A robot is going to attempt the same task 100 times. Each time it tries, it will either succeed or fail to succeed in completing the task. Say the robot does not learn from its tries, so each attempt at the task is independent of the others. On a given attempt, the probability of the robot succeeding is 0.85. Let X be the random variable of the number of times this robot is able to succeed in completing the task. part 1. What is the probability that the robot succeeds less than or equal to 80 times? (it is only for part a; no need to show work) a. Use the compliment rule to reduce the number of operations needed in part 1. Find another way to compute the needed probability. b. Now say two robots are going to attempt the same task. The robots operate independently from one another. What is the probability that both robots succeed less than or equal to 80 times out of 100? c. Now say the single robot begins to learn the more it tries. That is to say, it gets better at succeeding at…A bag contains 3 gold marbles, 9 silver marbles, and 24 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $4. If it is silver, you win $2. If it is black, you lose $1. What is your expected value if you play this game? Question Help: D Video Submit Question ype here to search ***_ F12 PriSc F10 F11 F7 F4 F3 % %23 7 4 2 P IT Y K G M C All Alt LL.Assume that the vaccine is given to a group of 50 people from Jamaica, what is the probability that it is an effective in exactly 40 persons? Interpretation your result
- A diagnostic test for disease X correctly identifies the disease 95% of the time. False positives occur 12%. It is estimated that 0.18% of the population suffers from disease X. Suppose the test is applied to a random individual from the population. Compute the following probabilities. (It may help to draw a probability tree.) The percentage chance that the test will be positive = % The probability that, given a positive result, the person has disease X = %A marksman takes 10 shots at a target and has probability 0.2 of hitting the target with each shot, independently of all other shots. Let ? be the number of hits. What is the probability of scoring no hits? Find the expectation and variance of ?.Roll a fair die (uniform 1,2,3,4,5,6) repeatedly. You and Peter are betting on the number shown on each roll. If the number is 4 or less, you win $1; otherwise, you pay Peter $2.5. a) What is the expected value of the payoff for you? b) What is the variance of your payoff?