Suppose Fx 183x2 8x 412 2 x 6 is the cdf for the random

Suppose F(x) = (1/8)(3x^2 - 8x + 4)^(1/2), 2 ? x ? 6, is the c.d.f. for the random variable X. Find (a) P (X ? 5), (b), P(3 < X < 4), and (c) the p.d.f. of X.

Please explain the steps to get the answer to these problems. Thanks!

F(x) = (1/8)(3x^2 - 8x + 4)^(1/2), 2 <= x <= 6,

F(6) = 1/8 (108-48+4)^(1/2) = 1

F(x) is a cdf

a) P(X<5) = F(5) = rt39/8

b) P(3 < X < 4) = F(4)-F(3) = 1/8(21-8+4) ^1/2= rt17/8

c) f(x) = pdf of x= derivative of F

= (3x-4)/4, 2<=x<=6

Suppose F(x) = (1/8)(3x^2 - 8x + 4)^(1/2), 2 ? x ? 6, is the c.d.f. for the random variable X. Find (a) P (X ? 5), (b), P(3 < X < 4), and (c) the p.d.f. o

Suppose Fx 183x2 8x 412 2 x 6 is the cdf for the random

Solution

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