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Define the following theorems with respect to a random vector

i) Central limit theorem

ii) Weak law of large numbers


Consider how DNA transcription is controlled. How could a PNA be used to serve a similar function?


inverse of 1 2 3

4 5 3

7 8 9


The output should be N lines containing the triangle pattern. Explanation For example,if the given number is 5,the pattern should be printed in 5 lines,as shown below



Question 2 [25] Suppose that the latest census indicates that for every 10 young people available to work only 4 are employed. Suppose a random sample of 20 young graduates is selected. Required: a) What is the probability that they are all employed? b) What is the probability that none of them are employed? c) What is the probability that at least four are employed? d) What is the probability that at most fifteen are employed? e) What is the probability that the number of young graduates who are employed is greater than ten but less than fifteen? f) What is the expected number of graduates who are not employed? g) What is the standard deviation for the number of graduates who are not employed?


Write a program using one dimensional arrays that searches a number and display the number of times it occurs on the list of 12 input values

Assume that X has a uniform distribution over [0; 1] and that Y has the uniform distribution over


[2; 3]: Which of the following statements are true and which are false? Justify your answers!


(a) P (X < Y) = 1.


(b) Since X is smaller than Y , P (X < 1) > P (Y < 1).


(c) There are some values a for which P (X < a) = P (Y < a).

if the hydrogen ion concentration is 4.7 x 10-8 what is the ph


Explain what you consider to be the positive and negative aspects of cloning both scientifically

survey of 31 randomly selected students finds that they save a mean of $82 per semester by

using a website. Assume the date comes from a normal distribution and the sample standard deviation is $18 per month.


Confidence Interval: What is the 99% confidence interval to estimate the population mean? (Round your

answers to two decimal places.)


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