12 pts Suppose that the cdf of a continuous random variable

(12 pts) Suppose that the c.d.f of a continuous random variable X is given (a) P(X 1.5) (c) P(X 6)

Solution

a)

As 2.8 is between 0 and 5,

P(x < 2.8) = 0.25(2.8) = 0.7 [answer]

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b)

P(x > 1.5) = 1 - P(x < 1.5) = 1 - 0.25(1.5)

= 0.625 [answer]

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c)

as x = -2 < 0,

P(x<-2) = 0 [answer]

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As x = 6 > 5

P(x > 6) = 1 [answer]