The randomnumber generator on calculators randomly generates

The random-number generator on calculators randomly generates a number between 0 and 1 The random variable X, the number generated follows a uniform probability distribution. Identify the graph of the uniform density function. What is the probability of generating a number between 0.72 and 0.94? What is the probability of generating a number greater than 0.86? The probability is . (Simplify- your answer.)

Solution

PDF of Uniform Distribution f(x) = 1 / ( b - a ) for a < x < b
b = Maximum Value
a = Minimum Value
Mean = a + b / 2
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 )

a)
p.d.f
f(x) = 1/(b-a) = 1 / (1-0) = 1 / 1 = 1
Option A

Mean = a + b / 2 = 0.5
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 ) = 0.289
b)
To find P(a < X < b) =( b - a ) * f(x)
P(0.72 < X < 0.94) = (0.94-0.72) * f(x)
= 0.22*1
= 0.22

c)
P(X > 0.86) = (1-0.86) * f(x)
= 0.14*1
= 0.14