Question : Find the expected value of the random variable whose density function is f(x) = (3/8)x^2 : 2163581
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
For the given probability density function, over the stated interval, find the requested value.
1) f(x) = (1/7), over the interval 2 ≤ x ≤ 8. Find E(x).
A) (60/7)
B) (59/14)
C) 24
D) (30/7)
2) f(x) = (1/5)x, over the interval 1 ≤ x ≤ 3. Find E(x).
A) (9/5)
B) (1/2)
C) (26/15)
D) (5/3)
3) f(x) = (1/7)x2, over the interval -2 ≤ x ≤ 3. Find E(x).
A) (73/28)
B) (81/28)
C) (71/28)
D) (65/28)
4) Find the expected value of the random variable whose density function is f(x) = (3/8)x2, 0 ≤ x ≤ 2.
A) (5/2)
B) (3/8)
C) (3/2)
D) (5/8)
E) none of these
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
5) Find the expected value and variance for the random variable whose probability density function is f(x) = x, 0 ≤ x ≤ 1.
Enter just two reduced fractions (unlabeled) in the order E(X), Var(X) separated by a comma.
6) Find the expected value and variance for the random variable whose probability density function is f(x) = (1/3), 2 ≤ x ≤ 5.
Enter just two reduced fractions of form (a/b) (unlabeled) in the order E(X), Var(X) separated by a comma.
7) Find the expected value and variance for the random variable whose probability density function is f(x) = 3x2, 0 ≤ x ≤ 1.
Enter just two reduced fractions (unlabeled) in the order E(X), Var(X) separated by a comma.
8) Find the expected value and variance for the random variable whose probability density function is f(x) = 12x2(1 - x), 0 ≤ x ≤ 1.
Enter just two reduced fractions (unlabeled) in the order E(X), Var(X) separated by a comma.
9) Find the expected value and variance for the random variable whose probability density function is f(x) = 2(x - 1), 1 ≤ x ≤ 2.
Enter just two reduced fractions (unlabeled) in the order E(X), Var(X) separated by a comma.
10) Find the expected value and variance for the random variable whose probability density function is f(x) = ex, x ≤ 0. (You may use the fact that 
beb = 0 .)
Enter just two integers (unlabeled) in the order E(X), Var(X) separated by a comma.
11) Find the expected value and variance for the random variable whose probability density function isf(x) = 4x - 1, (1/2) ≤ x ≤ 1.
Enter just two reduced fractions (unlabeled) in the order E(X), Var(X) separated by a comma.
12) A hardware store will cut lumber any length between 5 and 20 feet. Say X is the length of lumber requested by a customer. Then X is a uniform random variable with probability density function f(x) = (1/15). Find E(X) and Var(X).
Enter just two reduced fractions (unlabeled) in the order E(X), Var(X) separated by a comma.
13) The life of a battery is a random variable with probability density function f(x) = (3/56)x2, 2 ≤ x ≤ 4 where x is the time in months. Calculate E(X).
Enter just a reduced fraction of form (a/b) unlabeled.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Let X be a continuous random variable on a ≤ x ≤ b with probability density function f(x). Then the median of the x-values is that number m for which
Find the median.
14) f(x) = (1/8); 2 ≤ x ≤ 10
A) 2
B) (14/3)
C) 6
D) 8
15) f(x) = (x/8) - (5/8); 5 ≤ x ≤ 9
A) 0.50
B) 7.83
C) 7
D) 6.41
16) Suppose X is a normal random variable with density function f(x) = (1/√(2π))e(-1/2)(x + 4)2. Find the expected value and standard deviation of X.
A) μ = -4, σ = 16
B) μ = 4, σ = 1
C) μ = -4, σ = 1
D) μ = 1, σ = 16
E) μ = 1, σ = 4
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
17) Find (by inspection) the expected value and the variance of the random variables with the following density function: f(x) = 0.2e-0.2x, x ≥ 0
Enter your answer as just two integers separated by a comma, the first representing E(X) and the second representing Var(X).
18) Find (by inspection) the expected value and the variance of the random variables with the following density function: f(x) = (1/4√(2π))e-(1/2)[(x - 1)/4]^2, -∞ < x < ∞
Enter your answer as just two integers separated by a comma, the first representing E(X) and the second representing Var(X).
19) Find (by inspection) the expected value and standard deviation of the random variable with the following density function: f(x) = e-0.1x.
Enter your answer as just two integers separated by a comma, the first representing E(X) and the second representing √(Var(X)).
20) Find (by inspection) the expected value and standard deviation of the random variable with the following density function: f(x) = (1/2√(2π))e-1/8x^2
Enter your answer as just two numbers (integers or reduced fractions) separated by a comma, the first representing E(X) and the second representing √(Var(X)).
