32. If you buy a lottery ticket in 50 lotteries, in each of which your chance of...

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32. If you buy a lottery ticket in 50 lotteries, in each of which your chance of winning a prize is 1 100 , what is the (approximate) probability that you will win a prize (a)

at least once,

(b) exactly once,

(c) at least twice?

33. Let X be a random variable with probability density f (x) =

c(1 − x2), −1 < x < 1 0, otherwise

(a) What is the value of c?

(b) What is the cumulative distribution function of X?

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