Question: 5. The continuous random variable X has probability density function (), where () = 2(1 ), 0 < < 1 Obtain an expression for (

5. The continuous random variable X has probability density function (), where () = 2(1 ), 0 < < 1 Obtain an expression for ( ). Hence find the mean and the variance of = (1 ).

6. Given that X is normally distributed with mean 2.86 and standard deviation 1.2, find approximate values, to 3 decimal places for: (i) ( < 3.5) (ii) (( > 1.75) (iii) (3.1 < < 3.5) (iv) ( < < 3.08)

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