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For Question 9 to Question 11 on this page, use the information given as follows. A soccer stands in front of a line and kicks a football with a random angle. Assume that the point where the football hits the line is a random variable X, with the cdf given by $$G(z) = \frac{1}{\pi} (arctan z + \frac{\pi}{2}), -\infty < z < +\infty$$ What is the pdf g(x) of X? $$g(x) = \frac{1}{\pi(1+x^2)} + \frac{1}{2}$$ $$g(x) = \frac{1}{\pi(1+x^2)}$$ $$g(x) = \frac{1}{1+x^2} + \frac{1}{2}$$ $$g(x) = \frac{1}{1+x^2} + \frac{1}{2}$$ Non among the others Question 10 Not yet answered Marked out of 9.00 Flag question Using the result in Question 9, determine $$E[ln(1+X^2)]$$ . Hint: Use the following formulae: $$-\int_{-\infty}^{+\infty} g(x) ln[g(x)]dx = ln (4\pi)$$ ln 4 ln(4x) None among the others ln π It does NOT exist. Question 11 Not yet answered Marked out of 9.00 Flag question Define a function f(z) by $$f(z) = \frac{ln z}{1+z^2}, 0 < z < +\infty$$ Consider the following statements, where X is the random variable described in Question 9. (a) the expectation of X does NOT exist (b) the function f(x) defined above is a well-defined pdf for a random variable (c) Var(X) = 1 (d) The median of X, i.e. the value of t for which P(X ≤ t) = 1/2, is 1/2 Which statement/s above is/are correct? Choose 'Non among the others', if (a) - (d) are all wrong. All (a) - (d) Only (a) Only (a) and (b)

Name: for question 9 to question 11 on this page use the information given as follows a soccer stands in front of a line and kicks a football with a random angle assume that the point where the fo 60529
Uploaded: 2022-09-29T13:46:03-08:00
Duration: 3 min 51 s
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Description: for question 9 to question 11 on this page use the information given as follows a soccer stands in front of a line and kicks a football with a random angle assume that the point where the fo 60529

          For Question 9 to Question 11 on this
page, use the information given as
follows.
A soccer stands in front of a line and
kicks a football with a random angle.
Assume that the point where the
football hits the line is a random variable
X, with the cdf given by
$$G(z) = \frac{1}{\pi} (arctan z + \frac{\pi}{2}), -\infty < z < +\infty$$
What is the pdf g(x) of X?
$$g(x) = \frac{1}{\pi(1+x^2)} + \frac{1}{2}$$
$$g(x) = \frac{1}{\pi(1+x^2)}$$
$$g(x) = \frac{1}{1+x^2} + \frac{1}{2}$$
$$g(x) = \frac{1}{1+x^2} + \frac{1}{2}$$
Non among the others
Question 10
Not yet answered
Marked out of 9.00
Flag question
Using the result in Question 9, determine
$$E[ln(1+X^2)]$$ . Hint: Use the
following formulae:
$$-\int_{-\infty}^{+\infty} g(x) ln[g(x)]dx = ln (4\pi)$$
ln 4
ln(4x)
None among the others
ln π
It does NOT exist.
Question 11
Not yet answered
Marked out of 9.00
Flag question
Define a function f(z) by
$$f(z) = \frac{ln z}{1+z^2}, 0 < z < +\infty$$
Consider the following statements,
where X is the random variable
described in Question 9.
(a) the expectation of X does NOT
exist
(b) the function f(x) defined above
is a well-defined pdf for a random
variable
(c) Var(X) = 1
(d) The median of X, i.e. the value
of t for which P(X ≤ t) = 1/2, is
1/2
Which statement/s above is/are correct?
Choose 'Non among the others', if
(a) - (d) are all wrong.
All (a) - (d)
Only (a)
Only (a) and (b)

for question 9 to question 11 on this page use the information given as follows a soccer stands in front of a line and kicks a football with a random angle assume that the point where the fo 60529

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