Suppose a continuous R.V. x has 5(x)= (1-x*) for 0 0.5) Using distribution function, determine the probabilities that x is less than 0.3 between 0.4 and 0.6 Calculate mean and variance for the probability density function.

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Sunpose a continuous R.V. x has the probability density function
Sa(1-x²)
for 0<x<1
f (x)=-
%3D
elsewhere
Find k
b) Find P(0.1 <x< 0.2)
(c)
P(x > 0.5) Using distribution function, determine the probabilities that
) x is less than 0.3
e)
between 0.4 and 0.6
Calculate mean and variance for the probability density function.
Transcribed Image Text:Sunpose a continuous R.V. x has the probability density function Sa(1-x²) for 0<x<1 f (x)=- %3D elsewhere Find k b) Find P(0.1 <x< 0.2) (c) P(x > 0.5) Using distribution function, determine the probabilities that ) x is less than 0.3 e) between 0.4 and 0.6 Calculate mean and variance for the probability density function.
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