Question

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**?

Answer #1

True or False: The density value f(x) of a continuous random
variable is a probability that can take values between 0 and 1

- Determine the cumulative distribution function for the
random variable with probability density function ?(?) = 1 − 0.5?
for 0 < ? < 2 millimeters.
- Determine the mean and variance of the random variable
with probability density function

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 ).

If the probability
density of a random variable is given by f(x) =
Find the value of
k and the probabilities that a random variable having this
probability density will take on a value
(a) between 0.1
and
0.2 (b)
greater than 0.5.

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 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.

For a discrete random variable, the probability of the random
variable takes a value within a very small interval must be
A.
zero.
B.
very small.
C.
close to 1.
D.
none of the above.
QUESTION 10
The area under the density function in a certain interval of a
continuous random variable represents
A.
randomness.
B.
the area of one rectangle.
C.
the probability of the interval.
D.
none of the above.
QUESTION 11
For any random variable, X, E(X)...

If the probability density function of a random variable X is
ce−5∣x∣ , then (a) Compute the value of c. (b) What is the
probability that 2 < X ≤ 3? (c) What is the probability that X
> 0? (d) What is the probability that ∣X∣ < 1? (e) What is
the cumulative distribution function of X? (f) Compute the density
function of X3 . (g) Compute the density function of X2 .

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.

For probability density function of a random variable X, P(X
< a) can also be described as:
F(a), where F(X) is the cumulative distribution function.
1- F(a) where F(X) is the cumulative distribution function.
The area under the curve to the right of a.
The area under the curve between 0 and a.

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