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The​ random-number generator is used to generate a real number at random between 0 and​ 1, equally likely to fall anywhere in this interval of values.​ (For instance, 0.3794259382... is a possible​ outcome.) a. Sketch a curve of the probability distribution of this random variable. b. What is the mean of this probability​ distribution? c. Find the probability that the random number falls between 0.35 and 0.6. d. Find the probability that the random number is less than 0.81.

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Immaculata

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Step-by-step explanation:

f(x)=1, 0 < x < 1 is the probability density function of the random variable x.

generally, it is f(x)=1/(b-a)  a < x < b;

where b=1 and a=0.

b) mean = integral (0 to 1) xdx  = [tex]\frac{x^{2} }{2}[/tex] (0 to 1)  = 1/2

c)integral( 0.35 to 0.6) dx  =x (between 0.35 and 0.6)  = 0.6-0.35=0.25

d) integral(less than 0.82)dx = x (between 0 and 0.81) = 0.81 - 0 = 0.81

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