Miss Leo buys one mini lottery everyday. For every lottery she buys, it costs $1 and it has 0.001 to win the prize with value $200. (a) Miss Leo starts buying the lottery since Day 1. Let N be the first day(counting from Day 1) she wins the lottery. What is the distribution of N? Specific the parameter. Find also the expected value of N. (b) Let X be the count of lotteries that won by Miss Leo in two years (2 × 365 = 730 days). Explain why X can be approximated as a Poison random variable. Specify the parameter (i.e., the rate) of the Poison distribution. (c) Use the approximation from (b) to estimate the probability that Miss Leo wins > 1 lottery in two years. (d) Let Z be the net profit after two years (the difference of the total prize she earns and the total cost of lotteries). Find E [Z].
Probability ques
Miss Leo buys one mini lottery everyday. For every lottery
she buys, it costs $1 and it has 0.001 to win the prize with value $200.
(a) Miss Leo starts buying the lottery since Day 1. Let N be the first day(counting from Day 1) she wins the lottery. What is the distribution of N? Specific the parameter. Find also the expected value of N.
(b) Let X be the count of lotteries that won by Miss Leo in two years
(2 × 365 = 730 days). Explain why X can be approximated as a Poison random variable. Specify the parameter (i.e., the rate) of the Poison distribution.
(c) Use the approximation from (b) to estimate the probability that Miss Leo wins > 1 lottery in two years.
(d) Let Z be the net profit after two years (the difference of the total prize she earns and the total cost of lotteries). Find E [Z].
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