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 a x b and all of the values of x are equally likely to occur. The graph of the uniform distribution is shown below. The probability density function of a uniform distribution is shown too. Show that the probability density function of a uniform distribution satisfies the two conditions for a probability density function.

y=1/b-a

1)VERIFY THE AREA UNDER THE CURVE IS EQUAL TO 1. Choose the correct.

A) the area under the curve is the area of the rectangle (b-a)(1/b-a)=1

B) The area under the curve is two times the mean 2(b-a)/2=1

C)The area under the curve is the sum of the max and min a+b=0+1=1

2) Show that the value of the function can never be negative. Choose below

A) The denominator of the probability density function is always position because a<b, so b-a>0,

B) The value of b-a is less than one, therefore the value of the function must always be greater than 1

C)The numerator of the probability density function is 1 so the function must always be positive

Explanation / Answer

1) A) The area under the curve is the area of the rectangle (b-a)(1/b-a)=1

2) A) The denominator of the probability density function is always position because a<b, so b-a>0

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