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Stat400Lec10(Ch3.4,3.7)_ans - l\R&b cfw_t"nt R-i 7tF Stat...

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Review (3.3) {t"nt 7tF) o Continuous random variable and its c.d.f. o Probability density function (p.d.f.), its properties. o Mean, variance, moment generating function r Percentiles for p.d.f. o Comparison between discrete and continuous random variables Today's Lecture (3.4,3.7) r Uniform distribution, its mean, variance, m.g.f. o Exponential distribution and its mean, variance. r Memoryless properties of exponential distribution. o Cauchy distribution, GOT A MOMENT? Vo^r(X) - L(X- Mean, variance and m.g.f. of uniform distribution lf X - U(o.,b), then . E(x): ff,var(x) : q# o M(t) : E(etx) : ffi tt t I 0, 1 if , : 0. Example: Customers arrive randomly at a bank teller's window. Given that one customer arrived during a par- ticular 10-minute period, let X equal the time within the 10 minutes that the customer arrived. lf X - t/(0, 10), find r the p.d.f. of X o P(3 < X <7) Uniform distribution X has a uniform distribution on the interval [o, b] if X is equally likely to fall anywhere in the interval [a,b].
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