(a) Derive the method of finding the probability that exactly m among N events A1, A2,...

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(a) Derive the method of finding the probability that exactly m among N events A1, A2, ... AN occur simultaneously. Construct a problem and find the above probability for m-3 and N=5. (b) Define cumulative distribution function (cdf) and probability mass function (pmf) of a random variable. Suppose F(x)=0 if x < 0 = if 0 < x < 11 = 1 if x 11, where [x] largest integer less than or equal to x. Show that F is a cdf and find the pmf that it corresponds to. (c) Consider the distribution of a random variable X with probability density function f(x)=+ if 0, 0 (a) Derive the method of finding the probability that exactly m among N events A1, A2, ... AN occur simultaneously. Construct a problem and find the above probability for m-3 and N=5. (b) Define cumulative distribution function (cdf) and probability mass function (pmf) of a random variable. Suppose F(x)=0 if x < 0 = if 0 < x < 11 = 1 if x 11, where [x] largest integer less than or equal to x. Show that F is a cdf and find the pmf that it corresponds to. (c) Consider the distribution of a random variable X with probability density function f(x)=+ if 0, 0