# MATH 302 Lecture Notes - Lecture 1: Countable Set, Measuring Instrument

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Types of Random Variables

There are 3 types of random variables, Discrete, Continuous and Mixed.

Discrete are random variables with outcomes that are finite or if countably infinite.

What that means is that, on the number line, if the variable takes a particular value,

than there has to be some minimum difference between this value and the next value

the variable can take, so if a variable takes the value 1, and the minimum distance is 2,

then it can only take values of -1, 1 , 3 ,5 and so on.

Example: The number of 1’s I can get after rolling a dice 10 times, are discrete as the

values can only be 0,1,2 … 10 (that is there is a minimum difference of 1 between the

values that can be taken)

Continuous random values have outcomes whose range is an interval of real numbers

What that means is that, on the number line, the variable can take 2 values, which will

be the end points and then can take any value between those two values, even if the

distance between the values is infinitely small, so essentially there is no limit to the

distance between consecutive values, provided that they lie within the specified range.

Example: The length of a piece of string would be continuous, can take any value (if we

have an incredibly accurate measuring instrument) between 0 and some very large

value, say 1000000 miles.

Mixed random values have outcomes that show both Discrete and continuous

components.

13.6) 2 / 4

13.7 ) P(X = 1) = 1 / 6

P(X=2) = 1 /12

P(X=3) = 1 / 15

P(X = 4) = 1/30

13.8) 0.41 + 0.21 + 0.08 + 0.28 = 0.98

13.9) b) X = 0 = 0.3*0.5*0.6 = 0.090

c) 0.7*0.5*0.6 + 0.3*0.5*0.6 + 0.3*0.5*0.4

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