Given the probability distribution below. (a) Find P(X = 1). (b) Calculate the expected value E(X). X P(X) 0 0.08 1 2 0.42 3 0.38

Let X be a random variable with the following probability distribution. Value  x  of  X P(X=x) 0 0.25 10 0.20 20 0.10 30 0.35 40 0.10 Complete the following. (If necessary, consult a list of formulas.) (a) Find the expectation  E (X) of X .   E(X)=   (b) Find the variance Var (X)of X.   Var (X)=

Let X be a random variable with the following probability distribution.

Let X be a random variable with the following probability distribution. Value X of X P(X=x) 30 Continue 40 50 60 70 80 0.15 0.25 0.20 0.10 0.15 0.15 Complete the following. (If necessary, consult a list of formulas.) (a) Find the expectation E (X) of X. E (X) = (b) Find the variance Var(X) of X. Var(x) = 0 O S

Let X be a random variable with the following probability distribution. Value x of X P(X=x) 10 20 30 40 50 0.10 0.30 0.20 0.25 0.15 Complete the following. (If necessary, consult a list of formulas.) (a) Find the expectation E (X) of X. E (X) = 0 (b) Find the variance Var(X) of X. Var(x) =

Let X be a random variable with the following probability distribution. Value x of X P(X=x) 2 0.05 3 0.05 4 0.05 5 0.85 Complete the following. (If necessary, consult a list of formulas.) (a) Find the expectation E(X) of X. E (X) = 0 (b) Find the variance Var(X) of X. Var(x) = ☐ Check B X G

In each case, determine the value of the constant c that makes the probability statement correct. (Round your answers to two decimal places.)   (a) Φ(c) = 0.9850     (b) P(0 ≤ Z ≤ c) = 0.2995     (c) P(c ≤ Z) = 0.1314     (d) P(−c ≤ Z ≤ c) = 0.6528     (e) P(c ≤ |Z|) = 0.0128     You may need to use the appropriate table in the Appendix of Tables to answer this question.

Let X be a random variable with the following probability distribution. Value x of X P(X=x) 3 4 5 5.0 6 0.10 0.05 0.40 0.45 Complete the following. (If necessary, consult a list of formulas.) (a) Find the expectation E (X) of X. E (X) = 0 (b) Find the variance Var(X) of X. Var(x) = 0

Suppose that X and Y have the joint probability distribution shown to the right. (a) Find the marginal distribution of X. (b) Find the marginal distribution of Y. y f(x,y) 2 X 4 1 0.022 0.198 35 3 0.05 0.45 5 0.028 0.252