A penny and a nickel are tossed. Both are fair coins. Let X = 1 if the penny comes up heads, and let X = 0 otherwise. Let Y = 1 if the nickel comes up heads, and let Y = 0 otherwise. Let Z = 1 if both...

A penny and a nickel are tossed. Both are fair coins. Let X = 1 if the penny comes up heads, and let X = 0 otherwise. Let Y = 1 if the nickel comes up heads, and let Y = 0 otherwise. Let Z = 1 if both the penny and nickel come up heads, and let Z = 0 otherwise. a) Let p_X
denote the success probability for X. Find p_X. b) Let p_Y
denote the success probability for Y. Find p_Y. c) Let p_Z
denote the success probability for Z. Find p_Z. d) Are X and Y independent? e) Does p_Z
= p_Xp_Y? f) Does Z = XY? Explain.