Answer all the questions

1. Define the following: a) random variable b) probability distribution c) expected value 2. Three cards are drawn without replacement from the 12 face cards (jacks, queens, kings) of an ordinary deck of 52 playing cards. Let X be the number of kings selected and Y the number of jacks. Find the joint probability distribution of X and Y.3. A race car driver wishes to insure his car for the racing season for $50,000. The insurance company estimates a total loss may occur with probability 0.002, a 50% loss with probability 0.01, and a 25% loss with probability 0.1. Ignoring other partial losses, what premium should the insurance company charge each season to realize an average prot of $500? 4. Find the probability distribution for the number of tails that occur when 4 coins are tossed