15.) Consider the random variable X with density f(x) = (1/6)x 2 < x< 4 (a) Find E[X]. (b) Find E[X²]. (c) Find o? and o. Let X denote the amount in pounds of polyurethane cushioning found in a car. (See Exercise 4.) The density for X is given by 11 f(x) 25 < x< 50 In 2 x Find the mean, variance, and standard deviation for X. 17. Let X denote the length in minutes of a long-distance telephone conversation. The density for X is given by f(x) = (1/10)e-/10 (a) Find the moment generating function, mx(t). (b) Use my (t) to find the average length of such a call. (c) Find the variance and standard deviation for X. 18. (Uniform distribution.) The density for a random variable X distributed uni- formly over (a, b) is zi 1sd f(x). 1 -ima
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#17 b and c
![15.) Consider the random variable X with density
f(x) = (1/6)x
2 < x< 4
(a) Find E[X].
(b) Find E[X²].
(c) Find o? and o.
Let X denote the amount in pounds of polyurethane cushioning found in a car.
(See Exercise 4.) The density for X is given by
11
f(x)
25 < x< 50
In 2 x
Find the mean, variance, and standard deviation for X.
17. Let X denote the length in minutes of a long-distance telephone conversation.
The density for X is given by
f(x) = (1/10)e-/10
(a) Find the moment generating function, mx(t).
(b) Use my (t) to find the average length of such a call.
(c) Find the variance and standard deviation for X.
18. (Uniform distribution.) The density for a random variable X distributed uni-
formly over (a, b) is
zi 1sd f(x).
1
-ima<x< b
b – a
%3D
Use Definition 4.2.1 to show that
a + b
(b- a)2
and
Var X =
%3D
E[X]
12
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