A uniform distribution is a continuous probability distribution for a random var

Question

A uniform distribution is a continuous probability distribution for a random variable x between two values a and b (a<b), where axb and all of the values of x are equally likely to occur. The graph of a uniform distribution is shown to the right. The probability density function of a uniform distribution is shown below. Show that the probability density function of a uniform distribution satisfies the two conditions for a probability density function.

y = _1_

     ba

Verify the area under the curve is equal to 1. Choose the correct explanation below.

A. The area under the curve is sum of the maximum and minimum. 1a+b=0+1=1

B. The area under the curve is two times the mean. 2(ba)=1

2

C. The area under the curve is the area of the rectangle. (ba)[1ba]=1

Show that the value of the function can never be negative. Choose the correct explanation below.

A. The value of ba is less than one, therefore the value of the function must always be greater than 1.

B. The numerator of the probability density function is 1, so the function must always be positive.

C. The denominator of the probability density function is always positive because a less than

a<b , so ba>0 , therefore the function must always be positive.

y = _1_

     ba

Explanation / Answer

Area under the curve is equal to 1 because

C. The area under the curve is the area of the rectangle, (ba)x[1/(ba)]=1

The value of the function can never be negative because

C. The denominator of the probability density function is always positive because a<b , so ba>0 , therefore the function must always be positive

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