- Due Fri, Sept 12, 2014
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**Problem 1**: Suppose we have obtained the following measurements. Calculate the corresponding power, specificity and sensitivity.**Actual Condition****Absent (Ho is true)****Present (H1 is true)****Test Result****Negative(fail to reject Ho)**0.983 0.0025 **Positive (reject Ho)**0.0085 0.0055 **Problem 2**: Using R and SOCR, generate 100 random observations from uniform(-1,1), normal(0,1) and exponential(1) distributions. Then Use the SOCR QQ Data-Data Plot to compare the paired samples, i.e., for each distribution, plot the quantiles of the R-generated sample against the SOCR generated sample. What do you expect and what do you see? Explain.**Problem 3**: The Poisson distribution with parameter λ can be approximated with normal when λ is large. Suppose patients arrive at a hospital at a rate of 50 per day. Let’s assume that the process is a Poisson random variable with λ=50. Compute the probability that in the next day the number of patients that arrive at this hospital will be between 54 and 62. Use the SOCR Normal (N(μ=50,σ=7.071)) and Poisson (Poisson(λ=50))distribution calculators.**Problem 4**: Use the Vitamin K shots Neonate Infant Pain Score (NIPS) dataset and SOCR Charts to generate a box plot, a scatter plot, a line plot, a dot plot, a boxplot, a histogram plot and a pie chart for some of the variables (Immediate, 30_Sec_Later, 60_Sec_Later, 120_Sec_Later, Total_Cry_Time).