Question

1) You buy a lottery ticket to a lottery that costs $10 per ticket. There are only 100 tickets available to be sold in this lottery. In this lottery there are one $500 prize, two $100 prizes, and four $25 prizes.

Show its probability distribution in the form of a table.

What is the standard deviation of your gain or loss?

What type of skewness does the probability distribution represent?

Answer 1

let X represent the amount of winning money

probability distribution table-

X	P(X)
500	0.01
100	0.02
25	0.04
0	0.93

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X	P(X)	X*P(X)	X² * P(X)
500	0.01	5.000	2500.0000
100	0.02	2.000	200.0000
25	0.04	1.000	25.0000
0	0.93	0.000	0.0000

	P(X)	X*P(X)	X² * P(X)
total sum =	1	8	2725.00

mean = E[X] = Σx*P(X) =            8.0000
          
E [ X² ] = ΣX² * P(X) =            2725.0000
          
variance = E[ X² ] - (E[ X ])² =            2661.0000
          
std dev = √(variance) =            51.5849

so, standard deviation of loss = 51.5849

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the probability distribution is skewed to right.