Question

Identify the FALSE statement relative to a continuous random
variable, *x*, and its probability distribution:

Select one:

a. The distribution of *x* is modelled by a smooth curve
called a probability density function.

b. *P(x = a)* is given by the height of the density
function above the point, *a*.

c. The total area under the graph of the density function is 1.

d. The area above an interval and below the density curve gives
the probability of *x* lying in that interval.

Answer #1

The distribution of a continuous random variable is defined by an equation called probability density function. Hence, Option A seems right here.

The area bounded by the curve of the density function and the x-axis is equal to 1, when computed over the domain of the variable. Option C seems fine too.

The probability that a random variable assumes a value between
*a* and *b* is equal to the area under the density
function bounded by *a* and *b*. Option D is correct
as well.

Option B, which says the height of the density function above the point a defines the probability is incorrect. The probability is defined by the area covered by that point.

**Option B is the answer.**

__________ For a continuous random variable x, the area
under the probability distribution curve between any two x-values
is always _____.
Greater than 1 B) less than
zero C) equal to 1 D) in the
range zero to 1, inclusive
_________For a continuous random variable x, the total
area under the probability distribution curve of x is always
______?
Less
than1 B)
greater than
1
C) equal to
1
D) 0.5
___________ The probability that a continuous random
variable x...

1) With a normal probability distribution curve, identify which
statement is false:
>all the possible probabilities are
under the curve.
>the area under the curve is
<1
>the left side is a mirror image of
the right side of the curve
>the probability that an item could
have 5 grams less weight and 5 grams more weight is the same.
2) Asymptotic is the term used to show that the tails of a
normal distribution:
...

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.

Which of the following is always true for all probability
density functions of continuous random variables?
A. They have the same height
B. They are bell-shaped
C. They are symmetrical
D. The area under the curve is 1.0
Like the normal distribution, the exponential density function
f(x)
A. is bell-shaped
B. approaches zero as x approaches infinity
C. approaches infinity as x approaches zero
D. is symmetrical

Which of the following statements is not true about continuous
probability distributions?
Select one:
a. The probability of any event is the area under the density
curve over the range of values that make up the event.
b. The total area under the density curve must be exactly 1.
c. If X is a continuous random variable taking values
between 0 and 500, then
P(X > 200) = P(X ? 200).
d. There are no disjoint events in continuous probability...

a continuous random variable X has a uniform distribution for
0<X<40
draw the graph of the probability density function
find p(X=27)
find p(X greater than or equal to 27)

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)...

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 ).

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

Suppose that X is a continuous random variable with a
probability density function that is a positive constant on the
interval [8,20], and is 0 otherwise.
a. What is the positive constant mentioned
above?
b. Calculate P(10?X?15).
c. Find an expression for the CDF FX(x).
Calculate the following values.
FX(7)=
FX(11)=
FX(30)=

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