2. [50 pts] Using microarray technology, an estimate of a gene's expression in a cohort of...

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2. [50 pts] Using microarray technology, an estimate of a gene's expression in a cohort of subjects can often be approximated as normally distributed because the gene's expression is often averaged over multiple probes on the microarray. Thus, the central limit theorem applies. Use Python to complete all parts of the problem. a. Implement the following: i. Generate n=5 samples that are uniformly distributed numbers in the range of [0, 1] and compute the mean of these 5 numbers. ii. Repeat this step 1000 times to obtain 1000 means. iii. Plot a histogram of these 1000 values. iv. Calculate the mean and standard deviation of this distribution. v. Calculate the percentage of the 1000 values that are within 1, 2, and 3 standard deviations of the mean. vi. Using vertical lines overlaid on the histogram, indicate the values corresponding to 1, 2, and 3, standard deviations from the mean. b. Repeat part (a), using n=30 in step (i), i.e., generating 30 uniformly distributed numbers in the range of [0, 1]. Show all numerical answers and figures as were required for part (a). C. What are the similarities/differences between these two distributions with n=5 versus n=30? 2. [50 pts] Using microarray technology, an estimate of a gene's expression in a cohort of subjects can often be approximated as normally distributed because the gene's expression is often averaged over multiple probes on the microarray. Thus, the central limit theorem applies. Use Python to complete all parts of the problem. a. Implement the following: i. Generate n=5 samples that are uniformly distributed numbers in the range of [0, 1] and compute the mean of these 5 numbers. ii. Repeat this step 1000 times to obtain 1000 means. iii. Plot a histogram of these 1000 values. iv. Calculate the mean and standard deviation of this distribution. v. Calculate the percentage of the 1000 values that are within 1, 2, and 3 standard deviations of the mean. vi. Using vertical lines overlaid on the histogram, indicate the values corresponding to 1, 2, and 3, standard deviations from the mean. b. Repeat part (a), using n=30 in step (i), i.e., generating 30 uniformly distributed numbers in the range of [0, 1]. Show all numerical answers and figures as were required for part (a). C. What are the similarities/differences between these two distributions with n=5 versus n=30?