Question

The random variable X has probability density function:

f(x) =

ke^(−x) 0 ≤ x ≤ ln 2

0 otherwise

Part a: Determine the value of k.

Part b: Find F(x), the cumulative distribution function of X.

Part c: Find E[X].

Part d: Find the variance and standard deviation of X.

All work must be shown for this question. R-Studio should not be
used.

Answer #1

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 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.

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

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)

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.

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. 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=

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...

Suppose that the probability density function for the random
variable X is given by ??(?) = 1/5000 (10? 3 − ? 4 ) for 0 ≤ ? ≤
10
What is ?(?)?
What is ?????(?)
Provide the cumulative distribution function for the random
variable X.

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 .

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 3 minutes ago

asked 3 minutes ago

asked 4 minutes ago

asked 5 minutes ago

asked 10 minutes ago

asked 10 minutes ago

asked 15 minutes ago

asked 16 minutes ago

asked 16 minutes ago

asked 20 minutes ago

asked 22 minutes ago