A credit score is used by credit agencies (such as mortgage companies and banks) to assess the creditworthiness of individuals. Values range from 300 to 850, with a credit score over 700 considered to be a quality credit risk. According to a survey, the mean credit score is 705.4. A credit analyst wondered whether high-income individuals (incomes in excess of $100,000 per year) had higher credit scores. He obtained a random sample of 44 high-income individuals and found the sample mean credit score to be 719.1 with a standard deviation of 80.6. Conduct the appropriate test to determine if high-income individuals have higher credit scores at the a= 0.05 level of significance. State the null and alternative hypotheses. H₂H 705.4 H₁³µ > 705.4 (Type integers or decimals. Do not round.) Identify the t-statistic. to = (Round to two decimal places as needed.) =

1a) Derive a maximum-liklihood estimator for the unknown parameter Y 1b) An experienced sales person completes sales following a Poisson distribution, with a mean rate of Y = 1.8 sales/month. A junior sales person completes sales at a mean rate of Y = 0.85 sales per month  Find the probability of the joint sales team (experienced and junior)  completing exactly 2 sales in any given months, assuming the two sales people act independently of each other.  1c) Find the probability of the joint sales team (experienced and junior) completing more than 2 sales in any given months

Chains "A" and "B" are made of the same steel. "A" consists of three links and "B" consists of six links, each link having a normal distribution function of the resisting strength with a mean of 60,000 psi and standard deviation of 5,000 psi. Determine which chain is generally weaker (from a probabilistic point of view) by plotting the probability distribution functions of their resisting strengths on the same diagram.

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A disk drive has a constant failure rate and an MTTF of 5000 hr. (a) What will the probability of failure be for one year of operation? (b) What will the probability of failure be for one year of operation if two of the drives are placed in active parallel and the failures are independent? (d) What will the probability of failure be for one year of operation if the system si changed to standby model. (e) Describe the effect on the MTTF with a switching failure probability of 0.05. () What would be change in MTTF if the probability of failure of standby unit is 10 percent of the failure of the primary unit in the standby mode?

Exercise 2. A r.v. X is Poisson distributed with parameter λ = 5.5. (a) Calculate the probability that X = 3. (b) Calculate the probability that X < 2. (c) What is the most likely (i.e. highest probability) value for X ? (You can make a graph of f(x) to find the answer).