Workshop solutions for Math 103 Probability: Week 13
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1.
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(a)
A random variable is a function .
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(b)
The induced sample space is the range of values taken by the random variable defined on , that is .
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(c)
The probability mass function of a discrete random variable, , is defined by
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(d)
The cumulative distribution function of a random variable is a function given by
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(e)
The expected value of a discrete random variable is
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(f)
The variance of a random variable is
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(g)
The standard deviation of is the square root of the variance.
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(a)
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2.
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(a)
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(b)
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(a)
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3.
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4.
1-pbinom(2,size=20,prob=0.2)
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5.
Lack of memory in independent (biased) coin tosses, i.e. the information that you’ve had tails previously tells you no more information about how many further coin tosses you need to wait before you see a head.