Question

13. If X follows the following cumulative probability
distribution:

0 X≤5

0.10 (X-5) 5≤X≤7

F (X) 0.20 + 0.20 (X-7) 7≤X≤11

1 X≥11

a. Calculate a probability function f (X) (10 pts)

b. Calculate the expected value of X and the Variance of X. (15
pts)

c. Calculate the probability that X is between 6.0 and 8.80. (10
pts)

d. Calculate the percentile of 70 percent. (10 pts)

e. Calculate the expected g (x), if g (X) = 2X-10 (15
pts)

Answer #1

Given the following cumulative probability
function:
0 x < -5
.10 -5 <= x < 0
.40 0 <= x < 5
F(x)= .50 5 <= x < 10
.75 10 <= x < 15
1.0 X >= 15
a. P( 0 <x<10)
b. P( 5<x<10)
c. P(x< 10)
d. P(x>5)
e. P(x=7)
f. Calculate f (x) and draw F (x) and F (x)
g. Calculate E (x)
h. Calculate the variance of X
i. Calculate the expected g (x)...

Given the following probability function:
.10 x = 5
f(x) = . 20 x = -2, 8, 10
.30 x = 6
A. Calculate f(x) and make an appropriate drawing of f(x) and
F(x) (15 pts)
B. P (6 < X < 8) (5 pts)
C. P (x > 7) (5 pts)
D. P (x < 8) (5 pts)
E. The average of X (5 pts)
F. The fashion of X (5 pts)
G. The variance of X (10 pts)

Suppose that the random variable X has the following cumulative
probability distribution
X: 0 1. 2. 3. 4
F(X): 0.1 0.29. 0.49. 0.8. 1.0
Part 1: Find P open parentheses 1 less or equal than
x less or equal than 2 close parentheses
Part 2: Determine the density function f(x).
Part 3: Find E(X).
Part 4: Find Var(X).
Part 5: Suppose Y = 2X - 3, for all of X, determine
E(Y) and Var(Y)

Consider the following cumulative probability
distribution.
x
0
1
2
3
4
5
P(X ≤ x)
0.10
0.29
0.48
0.68
0.84
1
a. Calculate P(X ≤ 2).
(Round your answer to 2 decimal places.)
b. Calculate P(X = 2).
(Round your answer to 2 decimal places.)
c. Calculate P(2 ≤ X ≤ 4).
(Round your answer to 2 decimal places.)

Monthly demand for a product follows
the following probability distribution. Then find the expected
demand for the product and also
variance.
Demand
1
2
3
4
5
6
Probability
0.10
0.15
0.20
0.25
0.18
0.12

X is a continuous random variable with the cumulative
distribution function
F(x) = 0
when x <
0
= x2
when 0 ≤ x ≤
1
= 1
when x >
1
Compute P(1/4 < X ≤ 1/2)
What is f(x), the probability density function of X?
Compute E[X]

Consider the following probability distribution for stocks A and
B:
State
Probability
Return on Stock A
Return on Stock B
1
0.10
10%
8%
2
0.20
13%
7%
3
0.20
12%
6%
4
0.30
14%
9%
5
0.20
15%
8%
The coefficient of correlation between A and B is
(Hint: compute variance and covariance first.)
Group of answer choices
0.47.
none of the above.
0.60.
0.58
1.20.

Suppose we have the following probability mass function.
X
0
2
4
6
8
F(x)
0.1
0.3
0.2
0.3
0.1
a) Determine the cumulative distribution function, F(x).
b) Determine the expected value (mean), E(X) = μ.
c) Determine the variance, V(X) = σ^2

Suppose a random variable X has cumulative distribution function
(cdf) F and probability
density function (pdf) f. Consider the random variable Y =
X?b
a for a > 0 and real b.
(a) Let G(x) = P(Y x) denote the cdf of Y . What is the
relationship between the functions
G and F? Explain your answer clearly.
(b) Let g(x) denote the pdf of Y . How are the two functions f
and g related?
Note: Here, Y is...

The probability distribution function for the random variable X,
the lead content in a liter of gasoline is: (a) Prove that f(x) IS
a probability distribution function (b) Find the expected value of
lead content in a liter of gasoline (c) Find the standard deviation
of the lead content in a liter of gasoline (d) Find the equation
for the cumulative distribution function of X f(x) = 12.5x – 1.25,
0.10 < x < 0.50 0, elsewhere

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