Question

4. The density curve of X is the triangle shown below: a) What is the height of the triangle. b) What is the probability that x is less than 1?( Sketch the density curve, shade the area that represents the probability then fin the area. Do this for (c) also.) c) What is the probability that X is less than 0.5?

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Answer #1

4)

as area under a density curve is 1

therefore (1/2)*height*base =1

(1/2)*h*2=1

height =h= 1

b)P(X<1)=area of shaded region =(1/2)*1*1 =0.5

1 0 2 1

c)

P(X<0.5 ) =area of shaded region =(1/2)*0.5*0.5=0.125

0.5 0 0.5 1

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