Question

4. The probability of a set of outcomes X of a aindom process s ditributed in the rang 3-xs with the form f.(x)-3x /98 a- Find the probability of the set of outcomes X>4. b- Calculate E(X). c- Find a form for fx>4)

Answer 1

a)

f(x) = 3 x^2/98

P(X > 4)

$=\int _4^53\cdot \frac{x^2}{98}dx=\frac{61}{98}\quad \left(\mathrm{Decimal:\quad }\:0.62245\dots \right)$

b)

$E(X) = \int _3^53x\frac{x^2}{98}dx=\frac{204}{49}\quad \left(\mathrm{Decimal:\quad }\:4.16327\dots \right)$

c)

f(x|x > 4)

= f(x) / P(X > 4)

= 3x^2/98 /(61/98)

= 3x^2/61

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