The random-number generator on calculators randomly generates a number 0 and 1.

Question

The random-number generator on calculators randomly generates a number 0 and 1. The random variable X, the number generated, follows a uniform probability distribution. (a) Identify the graph of the uniform density function. (b) What is the probability of generating a number between 0.09 and 0.67? (c) What is the probability of generating a number greater than 0.83? (a) Choose the correct graph of the uniform density function below. (b) The probability is (simplify your answer.) (a) The probability is (simply your answer.)

Explanation / Answer

PDF = 1 / (b-a)

a=0

b=1

PDF = 1 / (b-a)

        = 1 / (1-0)

Part a)

The graph is (B)

Explanation: it will take 0 to 1 is x axis and 0 to 1 in y axis also.

Part b)

P ( 0.09 < x < 0.67 ) = (0.67 – 0.09)/(1-0)

                                   = 0.58 / 1

                                   = 0.58

Answer: 0.58

Part c)

P ( x > 0.83 ) = (1-0.83)/(1-0)

                       = 0.17/1

                       =0.17

Answer: 0.17

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