Suppose a certain type of small data processing firm is so s

Suppose a certain type of small data processing firm is so specialized that some have difficulty making a profit in their first year of operation. The probability density function that characterizes the proportion Y that make a profit is given by f(y) = {ky4(1-y)3 , 0

Solution

a)

Integral [k y^4 (1 - y)^3 dy] | (0,1) = 1

= k[ -x^8/8 + 3x^7/7 - x^6/2 + x^5/5 ]| (0,1)

= k (1/280) = 1

Thus,

k = 280 [ANSWER]

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b)

P(0<y<0.5) = 280 [ -x^8/8 + 3x^7/7 - x^6/2 + x^5/5 ]| (0,0.5)

= 0.36328 [answer]

**************

c)

P(0.8<y<1) = 280 [ -x^8/8 + 3x^7/7 - x^6/2 + x^5/5 ]| (0.8,1)

= 0.0562816 [answer]