Problem 3: Suppose X is a discrete random variable that takes on integer values between 1 and 10, with variance Var(X) = 6. Suppose that you define a new random variable Y by observing the output of X and adding 3 to that number. What is the variance of Y? Suppose then you define a new random variable Z by observing the output of X and multiplying that by -4. What is the variance of Z?

Suppose you would like to keep a test tube at 48F (exactly), but your refrigeration unit exhibits some random fluctuations, so that the difference between the temperature at which you set the thermostat and the true temperature is distributed normally with mean 0 and variance 1.96. What is the highest you can set the thermostat and be 95% sure that the true temperature is no more than 48F?

Suppose that we have disjoint normal populations A and B with unknown population variances. Suppose we have a sample of size 1O from from population A and a sample of size 15 from population B which we would like to pool to form the pooled variance. But, for this we need to assume that the population variances are equal. If the sample variance for the sample from population A is 11 and the sample variance for the sample from population B is 7, then does our data actually give evidence that the two population variances are actually different? Give the P-Value of this data as evidence that the two population variances are different (use stattrek.org). .44 1.56 .22 .78 NONE OF THE OTHERS

A nail is needed to hang up a 50 lb painting on a wall. A technician has two nails in his pocket, where the probability that both nails meet the specific weight of the painting is 50%, the probability that only one of them meets the specific weight is 20%, and the probability that neither of them meets the specific weight is 30%. If the number of nails that meet the specification is a random variable, find the variance of the data of that random variable.