MATHS ASSIGNMENT PROBLEMS

| August 30, 2017

Question
Find , , if a random variable is given by its density function, such that (25 points)

, if

, if

, if

Let be given by its distribution function F(x), such that

F(x) = 0 if x ? 0 (25 points)

F(x) = if 02

Graph the distribution function

Graph the density function

Find ,,

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A random variable is distributed normally with E(X) = 8 and ?(X) =3. Find P(9?X

Find the density function of a normally distributed random variable, if E(X) = 7.8 and ?(X) = 4.1 (5 points)

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It’s known that a random variable is distributed normally with E(X) = 3

and it’s also known that p(0?X?1)+p(5?X?6) = 0.6. Find p(p(5?X?6). (20 points)

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