Problem 3. (12 points) Let X denotes the amount of time a book on two-hour reserve...

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Problem 3. (12 points) Let X denotes the amount of time a book on two-hour reserve is actually checked out, and suppose the C

math Statistics-And-Probability

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Answer 1

Answer #1

1)

P(0.5<X<1)=F(1)-F(0.5)=(1²/4)-(0.5²/4)=0.1875

2)

P(X>1.5)=1-P(X<1.5)=1-1.5²/4 =0.4375

3)

mean = $\int_{0}^{2}$ (1-F(x)) dx = $\int_{0}^{2}$ (1-x²/4) dx =(x-x³/12)|²0 =4/3

4)

let median be a;

hence F(a)=0.5

a²/4=0.5

a=√2=1.4142

5)

pdf of X =f(x)=(d/dx)(F(x) =(d/dx)(x²/4)

f(x)=x/2 for 0 <x<2

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Answer 2

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Problem 3. (12 points) Let X denotes the amount of time a book on two-hour reserve...

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Problem 3. (12 points) Let X denotes the amount of time a book on two-hour reserve...

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