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Solution to 10. Determine the probability density function for the cumulative distribution function shown below. F {0, … - Sikademy
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Mirian Woke

10. Determine the probability density function for the cumulative distribution function shown below. F {0, x < −2 0.25x + 0.5, −2 ≤ x < 1 0.5x + 0.25, 1 ≤ x < 1.5 1 x > 1.5 Determine also the following probabilities. (a) P(X > −1) (b)P(X < 1.3) (c) P(−1.5 ≤ X ≤ 1.8) (d)P(X < 1.5)

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Here's the Solution to this Question

f(x) - density function, then f(x)=F'(x), so

f(x)=(0.25x+0.5)'=0.25, -2≤x<1

f(x)=(0.5x+0.25)'=0.5, 1≤x<1.5

f(x)=0, otherwise

a) P(X>-1)=1-P(X≤-1)=1-F(-1)=1-0.25*(-1)-0.5=0.75

b) P(X<1.3)=F(1.3)=0.5*1.3+0.25=0.9

c) P(-1.5≤X≤1.8)=F(1.8)-F(-1.5)=1-0.25*(-1.5)-0.5=0.875

d) P(x<1.5)=F(1.5)=1


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Question ID: mtid-4-stid-47-sqid-4353-qpid-72