Question

Let X be a continuous uniform (-2,5) random variable. Let W = |X| Your goal is...

Let X be a continuous uniform (-2,5) random variable. Let W = |X| Your goal is to find the pdf of W.

a)Begin by finding the sample space of W

b)Translate the following into a probability statement about X: Fw(w) = P[W <= w] = ....

c) Consider different values of W the sample of W. Do you need to break up the sample space into cases?

d)Find the cdf of W

e)Find the pdf of W

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Given that X~U(-2,5)

∴ f(x) = 1/(5-(-2)) = 1/7

a) Given W=|X|

Therefore, W can take positive values of X. i.e, the sample space of W is (0,5)

b) FW(W) = P(W<=w)

= P(|X|<=w)

= P(-w <= X <= w)

c) The sample values of W will be (0,5). Therefore, we need to break up the sample space into cases, w=0 and 0<w<5

d) cdf of W

FW(W) = P(W<=w)

= P(|X|<=w)

= P(-w <= X <= w)

=

=  

=  

e) pdf of f(x) = F'X(x)

= 2/7 , 0<w< 5

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