1. Let X have the probability density function f(x) = cr(1-r) for 0≤x≤1 and f(x) = 0 otherwise. (a) Show that c = 6. (b) Find the cumulative distribution function F(x) = P(X ≤ r). (c) Calculate P(.1 < X <.5). (d) Find the mean, variance and standard deviation of X.
1. Let X have the probability density function f(x) = cr(1-r) for 0≤x≤1 and f(x) = 0 otherwise. (a) Show that c = 6. (b) Find the cumulative distribution function F(x) = P(X ≤ r). (c) Calculate P(.1 < X <.5). (d) Find the mean, variance and standard deviation of X.
Chapter5: Exponential And Logarithmic Functions
Section5.5: Exponential And Logarithmic Models
Problem 4ECP
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Transcribed Image Text:1. Let X have the probability density function f(x) = cr(1-x) for 0≤x≤ 1 and f(x) = 0 otherwise.
(a) Show that c = 6.
(b) Find the cumulative distribution function F(x) = P(X ≤r).
(c) Calculate P(.1 < X < .5).
(d) Find the mean, variance and standard deviation of X.
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