Question

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)

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)...

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...

2.
2. The joint probability density function of X and Y is given
by
f(x,y) = (6/7)(x² + xy/2),
0 < x < 1, 0 < y < 2. f(x,y) =0
otherwise
a) Compute the marginal densities of X and Y. b) Are X and Y
independent. c) Compute the conditional density
function f(y|x) and check restrictions on function you derived d)
probability P{X+Y<1} [5+5+5+5 = 20]

Suppose that the joint probability density function of the
random variables X and Y is f(x, y) = 8 >< >: x + cy^2 0 ≤
x ≤ 1, 0 ≤ y ≤ 1 0 otherwise.
(a) Sketch the region of non-zero probability density and show
that c = 3/ 2 .
(b) Find P(X + Y < 1), P(X + Y = 1) and P(X + Y > 1).
(c) Compute the marginal density function of X and Y...

2.
The joint probability density function of X and Y is given
by
f(x,y) = (6/7)(x² + xy/2),
0 < x < 1, 0 < y < 2. f(x,y) =0
otherwise
a) Compute the marginal densities of X and Y. b) Are X and Y
independent. c) Compute the conditional density
function f(y|x) and check restrictions on function you derived d)
probability P{X+Y<1}

Q6/
Let X be a discrete random variable defined by the
following probability function
x
2
3
7
9
f(x)
0.15
0.25
0.35
0.25
Give P(4≤ X < 8)
ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ
Q7/
Let X be a discrete random variable defined by the following
probability function
x
2
3
7
9
f(x)
0.15
0.25
0.35
0.25
Let F(x) be the CDF of X. Give F(7.5)
ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ
Q8/
Let X be a discrete random variable defined by the following
probability function :
x
2
6...

The joint probability density function of x and y is given by
f(x,y)=(x+y)/8 0<x<2, 0<y<2 0 otherwise
calculate the variance of (x+y)/2

Probability density function of the continuous random variable X
is given by f(x) = ( ce −1 8 x for x ≥ 0 0 elsewhere
(a) Determine the value of the constant c.
(b) Find P(X ≤ 36).
(c) Determine k such that P(X > k) = e −2 .

2. Let the probability density function (pdf) of random variable
X be given by:
f(x) = C (2x -
x²),
for
0< x < 2,
f(x) = 0,
otherwise
Find the value of
C.
(5points)
Find cumulative probability function
F(x)
(5points)
Find P (0 < X < 1), P (1< X < 2), P (2 < X
<3)
(3points)
Find the mean, : , and variance,
F².
(6points)

1. f is a probability density function for the random
variable X defined on the given interval. Find the
indicated probabilities.
f(x) = 1/36(9 − x2); [−3, 3]
(a) P(−1 ≤ X ≤ 1)(9 −
x2); [−3, 3]
(b) P(X ≤ 0)
(c) P(X > −1)
(d) P(X = 0)
2. Find the value of the constant k such that the
function is a probability density function on the indicated
interval.
f(x) = kx2; [0,
3]
k=

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