The number of cars X, used for official business purposes on any given workday of two companies, A and B, are given below   Company A  X 1 2 3  f(x) .3 .4 .3   Company B  X 0 1 2 3 4  f(x) .2 .1 .3 .3 .1  Compare the 2 companies in terms of their mean number of cars and the standard deviation =√V(X).  b. Should the 2 companies maintain the same number of cars for official use? Explain with numerical support.  Can computers ‘think’? According to the Turing test, a computer can be considered to think if, when a person communicates with  it, the person believes he or she is communicating with another person instead of a computer. In an experiment at Boston’s  Computer Museum, a judge communicated with four computers and four other people. He was asked to distinguish between them. Assume that he cannot distinguish between the four computers and the four people, and so he makes random guesses. a. Let the random variable X represent the number of correct guesses of a judge. Determine the probability distribution function  of X.  Can we conclude that computers can think? Numerically support your answer.  There are 4 black balls, and 4 white ones in an urn. You pick 4 balls.   Let X be the number of black balls you get. What are the values of X and the probabilities associated with each value? b. Suppose you win PhP500 per black ball you get, and an extra PhP2000 if you get all 4 black balls. What is your expected gain?

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  1. The number of cars X, used for official business purposes on any given workday of two companies, A and B, are given below 

 Company A 

X 1 2 3 

f(x) .3 .4 .3 

 Company B 

X 0 1 2 3 4 

f(x) .2 .1 .3 .3 .1 

  1. Compare the 2 companies in terms of their mean number of cars and the standard deviation =√V(X).  b. Should the 2 companies maintain the same number of cars for official use? Explain with numerical support. 
  2. Can computers ‘think’? According to the Turing test, a computer can be considered to think if, when a person communicates with  it, the person believes he or she is communicating with another person instead of a computer. In an experiment at Boston’s  Computer Museum, a judge communicated with four computers and four other people. He was asked to distinguish between them. Assume that he cannot distinguish between the four computers and the four people, and so he makes random guesses. a. Let the random variable X represent the number of correct guesses of a judge. Determine the probability distribution function  of X. 
  3. Can we conclude that computers can think? Numerically support your answer. 
  4. There are 4 black balls, and 4 white ones in an urn. You pick 4 balls.  
  5. Let X be the number of black balls you get. What are the values of X and the probabilities associated with each value? b. Suppose you win PhP500 per black ball you get, and an extra PhP2000 if you get all 4 black balls. What is your expected gain? 
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