An example of a uniform distribution is f(x) = 1 for 0 lessthanorequalto x lesst

Question

An example of a uniform distribution is f(x) = 1 for 0 lessthanorequalto x lessthanorequalto 1. The mean of the distribution for this example is 0.5 and the standard deviation is approximately 0.29. The graph of the distribution for this example is a square with the height and width both equal to 1 unit. In general, the density function for a uniform distribution on the interval from x = a and x = b is given by f(x) = 1/b - a. The mean is a + b/2 and the standard deviation is squareroot (b - a)^2/12. Complete parts (a) through (c) below. (a) Verify that the area under the curve is 1. Choose the correct explanation below. A. The area under the curve is two times the mean, 2 middot 0.5 = 1. B. The area under the curve is the area of the square. 1 middot 1 = 1. C. The area under the curve is a + b = 0 + 1 = 1. (b) Find the probability that x falls between 0.25 and 0.5. The probability is (Type an integer or a decimal.) (c) Find the probability that x falls between 0.3 and 0.6. The probability is (Type an integer or a decimal.)

Explanation / Answer

Ans:

a)Option B is correct.

The area under the curve is the area of the square,1*1=1

b)a=0,b=1

Cummulative distribution function F(x)=(x-a)/(b-a)=(x-0)/(1-0)=x

Probability that x falls between 0.25 and 0.5=P(x<0.5)-P(x<0.25)=0.5-0.25=0.25

c)Probability that x falls between 0.3 and 0.6=P(x<0.6)-P(x<0.3)=0.6-0.3=0.3

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