Question
Asked Mar 8, 2019
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Let M, N be two independent random variables such that M~Unif(0,1) and N~
Expo()
(a) Find the joint pdf of (M, N).
(b) Consider the quadratic equation 2 2MzN0, with unknown z. Show
that the probability that x is real is approximately 0.1445
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Let M, N be two independent random variables such that M~Unif(0,1) and N~ Expo() (a) Find the joint pdf of (M, N). (b) Consider the quadratic equation 2 2MzN0, with unknown z. Show that the probability that x is real is approximately 0.1445

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Expert Answer

Step 1

Part (a):

Here, M ~ Unif (0, 1), N ~ Expo (1/2), which are independent. Thus, the joint pdf is:

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Step 2

Part (b):

Solve the quadratic equation:

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Step 3

Distribution of M2:

...
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Advanced Topics in Statistics

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