2. A particular drug therapy is known to have a 70% cure rate. For a drug trial consisting of 40 patients construct the Binomial distribution and the cumulative distribution. Graph both distributions. Find the probability that: a) 20 people are cured. b) More than 30 people are cured. c) Between 17 and 25 people (inclusive) are cured. d) 10 people or fewer are cured. e) How many people do you expect to be cured?
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- Assume that, with probability 0.8, It’s going to snow and/or I’m going to stay at home; and with probability 0.7, when it snows, then I stay at home. What is the probability of being truth that I am going to stay at home?For the Covid-19 pandemic, let’s make the following assumptions: (i) the natural infection rate is 20% (i.e., a person who is not vaccinated has 20% chance of being infected); (ii) the vaccine is 90% effective at preventing Covid-19 infection (i.e., a vaccinated person has only 2% chance of being infected); (iii) the probability of a random person being vaccinated is 60%. Without knowing whether or not a person is vaccinated, what is the probability that this person will be infected? Given that a person is infected, what is the conditional probability that this person is vaccinated?Consider two defaultable 1-year loans with a principal of $1 million each. The probability of default on each loan is 2.5%. Assume that if one loan defaults, the other does not. Assume that in the event of default, the loan leads to a loss that can take any value between $0 and $1 million with equal probability, i.e., the probability that the loss is higher than $ ? million is 1 − ?. If a loan does not default, it yields a profit equal to $20,000. Compute the 1-year 98% Value at Risk (VaR) and Expected Shortfall (ES) of a single loan.
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- A particular telephone number is used to receive both voice calls and fax messages. Suppose that 20% of the incoming calls involve fax messages, and consider a sample of 20 incoming calls. (Round your answers to three decimal places.) (a) What is the probability that at most 6 of the calls involve a fax message?(b) What is the probability that exactly 6 of the calls involve a fax message?(c) What is the probability that at least 6 of the calls involve a fax message?(d) What is the probability that more than 6 of the calls involve a fax message?Please solve the following problem. Quiz = Pass Quiz = Fail AI = Fail 0.1 0.2 AI = Pass 0.6 0.1 Mid = Pass Mid = Fail AI = Fail 0.2 0.2 AI = Pass 0.5 0.1 Suppose you have three events AI Grade, Quiz, and Mid. Here each event has two possible outcomes, either pass or fail. Additionally, given that AI Grade is observed, Quiz and Mid become independent of each other. Also, out of every 100 students, 30 students fail the AI course. Now, using the joint probability tables given, calculate P(AI Grade=Pass, Quiz=Fail, Mid=Fail).In a place called BW is well known for its weather. The weather condition is not extreme at all and many people want to migrate there only for the characteristic of the place. it rains on one fourth of the days. The local evening newspaper attempts to predict whether or not it will rain the following day. Three quarters of rainy days and four fifths of dry days are correctly predicted by the previous evenings paper. Given that this evenings paper predicts rain, what is the probability that it will actually rain tomorrow?