A random variable X has the probability function as given in the table below.  It is easy to verify that the expected value is 12.  Find the variance of X  X     P(X) 6     .25 12    .50 18   .25

Let T be a random variable. If E(T) = a +60, find an unbiased estimator of 0. Is the mean- squared error (MSE) of an unbiased estimator always smaller than the MSE of a biased estimator? Give an example to support your answer.

Which of the following is a true statement? A. The expected value is the most frequently occurring value of the random variable. B. Variance is always >=0 C. Variance can be negative D. F(x)=P(X=x)

Find the variance and standard deviation of the following random variable. Hint: start by writing the distribution for the random variable X2 . x P(X = x) 0 0.5 1 0.2 2 0.3

Trying to find variance. his equation is Prob(x)*[x-e(x)]^2. Just need an example to get me started.Original question is: A call center recieves an average of 10 calls per hour. Assuming the number of calls received follows the poisson distribution, determine the probability of each of the discrete outcomes below. Then calculate the variance component for each one using the standard formula for the variance of a discrete random variable. At the end, take the sum of both columns. Table: Poisson Distribution Table Calls Density Variance 0 0.00%   1 0.05%   2 0.23%   3 0.76%   4 1.89%   5 3.78%   6 6.31%   7 9.01%   8 11.26%   9 12.51%   10 12.51%   11 11.37%   12 9.48%   13 7.29%   14 5.21%   15 3.47%   16 2.17%   17 1.28%   18 0.71%   19 0.37%   20 0.19%   21 0.09%   22 0.04%   23 0.02%   24 0.01%   25 0.00%   26 0.00%   27 0.00%   28 0.00%   29 0.00%   30 0.00%   Sum 100.00%

Q2: A random variable X has a mean = 8, a variance o² = 9, and an unknown probability distribution. Find P(X-826).