Question
Asked Oct 23, 2019
for y> M/
the cumulative distribution
(d) Find the probability P(Y < M/2). How can tlll
the c.d.f. Fy?
found
(e) Does Y qualify either as a discrete or as a continuous random variable
Hint. When you write down probabilities, be careful with and <whea
matters. If you need inspiration, look at Example 3.20
Exercise 3.62. A little boy plays outside in the yard. On his own he would co
back inside at a random time uniformly distributed on the interval [0, 1]. (Let
take the units to be hours.) However, if the boy is not back inside in 45 minue
his mother brings him in. Let X be the time when the boy comes back inside
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for y> M/ the cumulative distribution (d) Find the probability P(Y < M/2). How can tlll the c.d.f. Fy? found (e) Does Y qualify either as a discrete or as a continuous random variable Hint. When you write down probabilities, be careful with and <whea matters. If you need inspiration, look at Example 3.20 Exercise 3.62. A little boy plays outside in the yard. On his own he would co back inside at a random time uniformly distributed on the interval [0, 1]. (Let take the units to be hours.) However, if the boy is not back inside in 45 minue his mother brings him in. Let X be the time when the boy comes back inside

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Exercises
a) Find the cumulative distribution function F of X.
(b) Find the mean E(X).
(c) Find the variance Var(X).
Hint. You should see something analogous in Exa
Exercise 3.63. A random variable X is symmetric if X
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Exercises a) Find the cumulative distribution function F of X. (b) Find the mean E(X). (c) Find the variance Var(X). Hint. You should see something analogous in Exa Exercise 3.63. A random variable X is symmetric if X

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check_circleExpert Solution
Step 1

Introduction:

Some properties of the continuous uniform distribution:

Probability density function (pdf):

If X ~ U (a, b), the pdf f (x) = 1/(ba); a < X < b.

Cumulative distribution function (cdf):

The cdf F (x) = (xa)/(ba); a < x < b.

Expectation:

The mean or expectation of X is, E (X) = (a...

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