Show that the following function satisfies the properties of a joint probability mass function. y fxy(x,y) 1 1 1/4 1.5 2 1/8 1.5 3 1/4 2.5 4 1/4 3 5 1/8 f(x, y) > and Ef(x., y) = i i

Verify that the function corresponding to the figure to the right is a valid probability density function. Then find the following probabilities: a. P(x 8) c. P(7 0 for all values of x and the total area under the density function above the x-axis is O D. (Type an integer or a decimal. Do not round.) the given function is a valid probability density function.

Show that the following function satisfies the properties of a joint probability mass function. y fxv (X, y) 1.0 1/4 1.5 2 1/8 1.5 3 1/4 2.5 4 1/4 3.0 1/8

(c) At a bus stop, there are two buses available (bus numbers 1 and 2). For i = 1,2, the waiting time until bus i arrives is denoted by T;, with T independent of T2, and T; has density function fr. (t) = X, exp(-1;t), t>0.