STATISTICS 342 - Homework Assignment #1Due Friday, January 22, 20101. Let Y be a uniform random variable withθ1= 0 andθ2= 1.(a) Using R, generate 10,000 observations ofY. Find the following statistics for your 10,000 obser-vations: minimum, maximum, mean and variance. For each statistic, give the theoretical valuethat the statistic should be approximately equal to. Then produce a probability histogram of the10,000 observations.Turn this histogram in with your assignment.Describe the histogram inwords.(b) Take the 10,000 observations ofYfrom part (a) and calculate the following variable:u= 3 +2y.Find the following statistics for your 10,000 observations of this new variable:minimum,maximum, mean and variance. Then produce a probability histogram of the 10,000 observationof this new variable.Turn in this histogram with your assignment.Describe the histogram inwords.(c) Based on your answers to part (b), what distribution do you believe the random variableU=3 + 2Ywill have? Explain your answer.
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Probability theory, probability density function, Histogram