(Step-by-Step) 3.A Assume that the random variable X A is normally distributed with mean and variance equal to 100 and 64 respectively. Assume also that the


Question: 3.A Assume that the random variable X A is normally distributed with mean and variance equal to 100 and 64 respectively. Assume also that the independent random variable X B is also normally distributed with mean and variance equal to 120 and 4 respectively.

  1. Let Y=3X B -X A . Find E(Y) and Var(Y). Then compute the probability that Y will be greater than 250. Draw the probability density function of Y, clearly and neatly, and show the area that corresponds to this probability.
  2. Let M A be the mean of a random sample of size 8 drawn from population A. Similarly let M B be the mean of a random sample of size 4 drawn from population B. Finally, let W=M B -M A . Find E(W) and Var(W). Then compute the probability that W will be smaller than 17.

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