In a game of cards you win $1 if you draw an even number, $2 if...

In a game of cards you win $1 if you draw an even number, $2 if you draw diamonds, $5 if you draw a king and $10 if you draw the queen of diamonds. You get nothing for any other card that you draw.

In any random draw, how much money should you expect to win?

What is the standard deviation of expected winnings?

Solutions

Expert Solution

Suppose, random variable X denotes amount of money (in dollars) gained.

It is given that $10 is won in case of queen of diamonds.

It is given that $5 is won in case of any of four kings.

It is given that $2 is won in case of any of 13 diamonds. However, for queen of diamonds another higher amount prize is there.

It is given that $1 is won in case of any of 5*4 = 20 even number cards. However, for 5 even number cards (2 , 4, 6, 8 and 10) of diamonds another higher amount prize is there.

For remaining of the cards, there is no prize money.

(a)

Expected win is given by

(b)

Variance is given by

So, standard deviation is given by

orchestra answered 1 year ago

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