Question: Define continuous random variable Y by the density function f ( y)=12(y 2 - y 3 ) for 0?y?1 and f(y) = 0 otherwise. a)

Define continuous random variable Y by the density function f ( y)=12(y 2 - y 3 ) for 0?y?1 and f(y) = 0 otherwise.

a) Verify that f(y) is a valid density function.

b) Determine the cumulative distribution function for Y. Hint: F(y) should be defined for all real values of y.

c) Determine P(Y?0.5) using the cumulative function from part (b).

Define continuous random variable Y by the density function f ( y)=12(y

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