Question

Let X be a continuous random variable with the probability density function f(x) = C x, 6 ≤ x ≤ 25, zero otherwise.

a. Find the value of C that would make f(x) a valid probability density function. Enter a fraction (e.g. 2/5): C =

b. Find the probability P(X > 16). Give your answer to 4 decimal places.

c. Find the mean of the probability distribution of X. Give your answer to 4 decimal places.

d. Find the median of the probability distribution of X. Give your answer to 4 decimal places.

Answer #1

(a) C is got by noting that the Total Probability = 1.

So,

we get:

between the limits 6 to 25.

Applying linits, we get:

So,

C = **2/589**

(b)

The Probability Density Function of X is given by:

,

6 X 25

between the limts 16 to 25.

Applying limits, we get:

P(X>16) = **0.6265**

(c)

The mean E(x) is given by:

,

between the limits 6 to 25.

Applying limits, we get:

E(X) = **17.4409**

(d)

The median got as follows:

between the limits 6 to x.

Applying limits, we get:

So,

x= **18.1797**

Consider a continuous random variable X with the probability
density function f X ( x ) = |x|/C , – 2 ≤ x ≤ 1, zero elsewhere.
a) Find the value of C that makes f X ( x ) a valid probability
density function. b) Find the cumulative distribution function of
X, F X ( x ).

1 (a) Let f(x) be the probability density function of a
continuous random variable X defined by
f(x) = b(1 - x2), -1 < x < 1,
for some constant b. Determine the value of b.
1 (b) Find the distribution function F(x) of X . Enter the value
of F(0.5) as the answer to this question.

Let X be the random variable with probability density function
f(x) = 0.5x for 0 ≤ x ≤ 2 and zero otherwise. Find the
mean and standard deviation of the random variable X.

Let X be a random variable with probability density function
f(x) = {3/10x(3-x) if 0<=x<=2
.........{0 otherwise
a) Find the standard deviation of X to four decimal
places.
b) Find the mean of X to four decimal places.
c) Let y=x2 find the probability density function
fy of Y.

Let the probability density function of the random variable X be
f(x) = { e ^2x if x ≤ 0 ;1 /x ^2 if x ≥ 2 ; 0 otherwise}
Find the cumulative distribution function (cdf) of X.

Let X and Y be two continuous random variables with joint
probability density function
f(x,y) =
6x 0<y<1, 0<x<y,
0 otherwise.
a) Find the marginal density of Y .
b) Are X and Y independent?
c) Find the conditional density of X given Y = 1 /2

Let X and Y be two continuous random variables with joint
probability density function f(x,y) = xe^−x(y+1), 0 , 0< x <
∞,0 < y < ∞ otherwise
(a) Are X and Y independent or not? Why?
(b) Find the conditional density function of Y given X = 1.(

Let X be a continuous random variable with a probability density function
fX (x) = 2xI (0,1) (x) and let it be the function´
Y (x) = e^−x
a. Find the expression for the probability density function fY (y).
b. Find the domain of the probability density function fY (y).

suppose x is a continuous random variable with probability
density function f(x)= (x^2)/9 if 0<x<3 0 otherwise
find the mean and variance of x

Suppose that X1 and X2 are independent continuous random
variables with the same probability density function as: f(x) = ( x
2 0 < x < 2, 0 otherwise. Let a new random variable be Y =
min(X1, X2,).
a) Use distribution function method to find the probability
density function of Y, fY (y).
b) Compute P(Y > 1).
c) Compute E(Y )

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 2 minutes ago

asked 3 minutes ago

asked 4 minutes ago

asked 6 minutes ago

asked 7 minutes ago

asked 7 minutes ago

asked 10 minutes ago

asked 12 minutes ago

asked 12 minutes ago

asked 17 minutes ago

asked 19 minutes ago