lect8 - ABOUT QUIZ I RANDOM VARIABLES EXPECTATION SOME...

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ABOUT QUIZ I RANDOM VARIABLES EXPECTATION SOME BASIC PROPERTIES OF EXPECTATION Outline ABOUT QUIZ I RANDOM VARIABLES Binomial Distribution; Geometric Distribution; etc. EXPECTATION SOME BASIC PROPERTIES OF EXPECTATION 1 / 14 Xinghua Zheng Lect 8: Random variables, expectation
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ABOUT QUIZ I RANDOM VARIABLES EXPECTATION SOME BASIC PROPERTIES OF EXPECTATION About Quiz I Time: Sep. 30, in class You may only bring pens, one simple scientific calculator and one A4 sheet of formulas. Only one simple scientific calculator per student is permitted to be used during the examination. NO EXCEPTIONS. Backup calculators will NOT be provided. Calculators may not be shared. No other electronic device (e.g., cell phone, iPad...) is allowed The exam covers material from lectures 1 – 7. Hwk 1 solution will be posted on Sep. 28, after the due time. 2 / 14 Xinghua Zheng Lect 8: Random variables, expectation
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ABOUT QUIZ I RANDOM VARIABLES EXPECTATION SOME BASIC PROPERTIES OF EXPECTATION Binomial Distribution; Geometric Distribution; etc. RANDOM VARIABLES A random variable is a function, say X , from a sample space S to the real numbers: A discrete random variable is a random variable that takes on finitely or countably many values. E.g., number of spots that come up on the roll of two dice; number of tosses needed to produce the first head; etc. Let X be a (discrete) random variable. For each value x that X can take, put p X ( x ) = P [ X = x ] = P [ { s S : X ( s ) = x } ] . p X is called the probability mass function of X ; for short, the pmf of X . Convention: use capital letters for random variables, and lowercase letters for the possible values 3 / 14 Xinghua Zheng Lect 8: Random variables, expectation
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ABOUT QUIZ I RANDOM VARIABLES EXPECTATION SOME BASIC PROPERTIES OF EXPECTATION Binomial Distribution; Geometric Distribution; etc. EXAMPLES (A) Roulette . A roulette table has 18 red numbers, 18 black numbers, and 2 green numbers.
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