Answers to the following questions should be calculated in Matlab and given to 4

Question

Answers to the following questions should be calculated in Matlab and given to 4 decimal places. Be careful not to introduce errors by rounding in any intermediate calculations as this may lead to an incorrect final answer Suppose that the diameters of particles in a sediment are distributed uniformly between 0.5 and 2.1 mm. Let D be the diameter of randomly chosen particle (a) Find E(D) (b) Find the standard deviation sd(D). (c) Find the proportion of particles with diameters between 0.6 and 1 mm

Explanation / Answer

since D is uniformly distributed as D~Uniform(a,b)

here a=0.5 and b=2.1

then pfd (D)=1/(b-a) and distribution function F(D)=P(D<=d)=(d-a)/(b-a)

(a) E(D)=(b+a)/2=(2.1+0.5)/2=1.3

(b)var(D)=(b-a)2/12=(2.1-0.5)2/12=2.56/12=0.2133

sd(D)=sqrt(var(D))=sqrt(0.2133)=0.4619D

(c)P(0.6<D<1)=P(D<1)-P(D<0.6)=(1-0.6)/(2.1-0.5)=0.25

required proportion is 0.25

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