B Compute PX 0 C Compute P1 X 1 Enter your answer to 4 dec

B) Compute P(X > 0)

C) Compute P(-1< X < 1) (Enter your answer to 4 decimal places)

D) Compute P(X < -1.1 or X > 1.1) (Round your answer to 4 decimal places.)

The error involved in making a certain measurement is a continuous rv X with the following pdf 0.09375(4 -x2) -2 sx 9375(4 x2)-2 sx s 2 rx) = otherwise (a) Sketch the graph of f(x) f(x) 0.6 f(x) 0.4 0.3 0.2 0.6 0.5 0.4 0.3 0.2 f(x) f(x) 0.6 0.5 0.4 0.3 0.2 0.6 0.5 0.4 0.3 0.2

Solution

a)

As we see,

f(x) = 0.09375(4-x^2)

f(x) = 0.375 - 0.09375x^2

Thus, the y intercept must be 0.375, so the answer is the LOWER LEFT OPTION.

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b)

P(X<0) = 0.5, by symmetry.

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c)

P(-1<x<1) = Integral [f(x)dx]|(-1,1)

= 0.375x - 0.03125x^3|(-1,1)

= 0.6875 [ANSWER]

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D)

P(-1.1<x<1.1) = Integral [f(x)dx]|(-1.1,1.1)

= 0.375x - 0.03125x^3|(-1.1,1.1)

= 0.7418125 [ANSWER]