The probability distribution of a discrete random variable x is shown in the following table: x 1 2 3 4 5 P(x)  0.22   0.22   0.37   0.05   0.14   The standard deviation σ of the random variable x is about:

The probability distribution of a random variable X is given in the table below: -4 -2 2 4 .1 .2 .3 .1 .3 P(X Compute the : Мean: (round to 1 place if necessary) Variance: (round to 2 places if necessary) Standard Deviation : |(round to 2 places if necessary)

Let X be a random variable with the following probability distribution: - 4 3 5 f(x) 0.6 0.3 0.1 Find the standard deviation of X. The standard deviation is . (Round to two decimal places as needed.)

The probability distribution of the number of students absent on Mondays, is as follows: X O 1 2 3 4567 f(x) 0.02 0.03 0.26 0.34 0.22 0.08 0.04 0.01 (a) What is the probability that more than 3 students are absent. (b) Compute the expected value of the random variable X. Interpret this expected value. (c) Compute the variance and standard deviation of the random variable X. (d) Compute the expected value and variance of Y : (e) Compute the covariance Cov(X, Y) = 7X+ 3. (f) What is the value of the ratio Cov(X,Y)/Var(X) ? (g) What is the value of Cov(X, Y)/Var(X) for Y = ß0 + ß₁X ? (For this exrcise, you can use excel. No need to show all calculations, just specify the formulas and present the final values.) (a) (b) (c) (d) (e) (f) (g)