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Let the random variable be the random of the amount won. The random variable may take on only two value, (0,3000). That is
There are five hundred tickets to be sold and only one ticket wins P3,000. Therefore, the probability that a ticket wins P3,000 is and the probability that a tickets wins nothing is .
We can write this as, and .
The expected value is given as,
To find the variance, we first find
The expected gain and the variance of your gain are 6 and 17964 respectively.