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Discrete Random Variables

Discrete Random Variables. To understand what we mean by a discrete random variable To understand that the total sample space adds up to 1 To understand the P(X=x) notation To use the P(X=x) notation to solve problems. Discrete Random Variables. Value is from an experiment in the real world.

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Discrete Random Variables

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  1. Discrete Random Variables • To understand what we mean by a discrete random variable • To understand that the total sample space adds up to 1 • To understand the P(X=x) notation • To use the P(X=x) notation to solve problems

  2. Discrete Random Variables Value is from an experiment in the real world The value is numerical X is a random variable (e.g. X = Heads on a coin) x is a particular variable (e.g. 1 head in 2 throws) P(X=x) would be the probability of throwing 1 head in 2 throws of a coin Possible outcomes can be shown in a sample space

  3. Are these Discrete Random Variables? The average lifetime of a light bulb Not discrete, as time is continuous The number of days in January No, not variable as there are always 31 The number of moves it takes to win a game of draughts Yes, as number of moves are whole numbers and it varies game by game

  4. Sample Space 3 coins are tossed and the number of heads, X, are recorded • Show the sample space • Write down the probability distribution • Write down the probability function Sample space HHH, THH, HTH, HHT, TTH, THT, HTT, TTT

  5. Probability distribution 3 coins are tossed and the number of heads, X, are recorded • Show the sample space • Write down the probability distribution • Write down the probability function Sample space HHH, THH, HTH, HHT, TTH, THT, HTT, TTT Note that the probabilities add up to 1

  6. Probability distribution 3 coins are tossed and the number of heads, X, are recorded • Show the sample space • Write down the probability distribution • Write down the probability function Sample space HHH, THH, HTH, HHT, TTH, THT, HTT, TTT P(X=x) = ⅛, for x = 0,3 ⅜, x = 1,2 0, otherwise

  7. Example A tetrahedral die is numbered 1,2,3,4. The die is biased. P(die landing on any number = k/x where k is a constant. • Find the value of k • Write down the probability distribution for X, the number the die lands on after a single roll K/1 + K/2 +K/3 +K/4 = 1 25k = 12 25k = 1 12 k = 12/25 12k + 6k + 4k + 3k = 1 12

  8. Example A tetrahedral die is numbered 1,2,3,4. The die is biased. P(die landing on any number = k/x where k is a constant. • Find the value of k • Write down the probability distribution for X, the number the die lands on after a single roll

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