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A number is chosen at random from the set 1, 2, 3, ... , 100 and another number is chosen at random from the set 1, 2, 3, ... , 50. What is the expected value of the sum and the expected value of the product?
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Solution  
Let the variable representing a number from the first set be "x" and a number from the second set be be "y" First Set In the experiment of choosing a number from the set of 100 numbers, there are 100 elementary events i.e. the events of choosing 1, choosing 2,... , choosing 100 All these elementary events are equally likely (since any of the 100 numbers can appear on choosing a number) and mutually exclusive (since appear of one of the numbers prevents the appearance of the other numbers). They are exhaustive events since they form all possible events in the experiment. Therefore probability of occurance of each elementary event i.e. getting each number is 1/100 The probability distribution of "x" would therefore be
Calculations for Mean and Standard Deviations
Second Set In the experiment of choosing a number from the set of 50 numbers, there are 50 elementary events i.e. the events of choosing 1, choosing 2,... , choosing 50 All these elementary events are equally likely (since any of the 50 numbers can appear on choosing a number) and mutually exclusive (since appear of one of the numbers prevents the appearance of the other numbers). They are exhaustive events since they form all possible events in the experiment. Therefore probability of occurance of each elementary event i.e. getting each number is 1/50 The probability distribution of "y" would therefore be
Calculations for Mean and Standard Deviations
⇒ Expectation of the distribution
Expectation of the sum of the two variables
Expectation of the product of the two variables

Credit : Vijayalakshmi Desu 