The random-number generator on calculators randomly generates a number between 0

Question

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. Draw the graph of the uniform density function. This will not be collected. What is the maximum height of this uniform probability distribution? Enter your answer as a number. Maximum height = _______________ What is the probability of generating a number between 0 and 0.2? P(0 lessthanorequalsto X lessthanorequalsto 0.2) = __________________ What is the probability of generating a number between 0.25 and 0.6? P(0.25 lessthanorequalsto X lessthanorequalsto 0.6) = _______________ What is the probability of generating a number greater than 0.95? P(X greaterthan 0.95) = ______________________

Explanation / Answer

( a )

                                                                                                                                            

( b )

Maximum height = 1

( c ) 0.2 / ( 1 – 0 ) = 0.2

Answer: 0.2

( d )

P ( 0.25 <= X <= 0.6 ) = (0.6 – 0.25 ) / ( 1 -0 ) = 0.35 / 1 = 0.35

Answer: 0.35

( e )

P ( x >0.95 ) = (1-0.95) / ( 1-0) = 0.05 / 1 = 0.05

Answer: 0.05

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