Question

Compute the mean and median for a random variable with the probability density function shown below.

Answer #1

The probability density function of the X random variable is
given as follows.
?? (?) = {?? − ?? ?> 00 ????? ??????????
Since Y = 1-2X, calculate the probability density function of the Y
random variable and specify the range in which it is defined.

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.

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.

In a probability density function, the probability of each value
of the random variable can be easily calculated and can take on any
value including zero.
True or False?

The diameter of a rivet (in mm) is a random variable with
probability density function ?(?) = { 3 4 (? − 9)(11 − ?) 9 < ?
≤ 11 0 ??ℎ?????? }
a. probability diameter less than 9.8
b.probability greater than 10.5
c. find the mean diameter
d. find variance and standard deviation of the diameters

A random variable X takes values between -2 and 4 with
probability density function (pdf)
Sketch a graph of the pdf.
Construct the cumulative density function (cdf).
Using the cdf, find )
Using the pdf, find E(X)
Using the pdf, find the variance of X
Using either the pdf or the cdf, find the median of
X

Determine the mean and variance of the random variable with the
probability density function
f(x)=1.6(1-.8x), 0<x≤1.25

Let X be a continuous random variable with the following
probability density function:
f(x) = e^−(x−1) for x ≥ 1; 0 elsewhere
(i) Find P(0.5 < X < 2).
(ii) Find the value such that random variable X exceeds it 50%
of the time. This value is called the median of the random variable
X.

Suppose a random variable has the following probability density
function: f(x)=3cx^2 (1-x) 0≤x≤1
a) What must c be equal to for this to be a valid density
function?
b) Determine the mean of x, μ_x
c) Determine the median of x, μ ̃_x
d) Determine: P(0≤x≤0.5) ?

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