Construct a table with the probability distribution

Question

Question: Consider the following Table:

Y         0         1          2        3

P(Y)    0.10    0.30     0.40

a) Complete the Table with the probability of P(X = 3).

b) Calculate the mean, variance and standard deviation of Y.

c) Suppose now we have a new random variable X = 2 + 3Y. Construct a Table with the probability distribution of X for each value of Y and X.

d) Calculate the mean, variance and standard deviation of X.

e)  Use the properties of the expected value and variance to obtain the ex­pected value of X, E(X), and the variance of X, V(X). Compare your answers.