Question

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)

Answer #1

TOPIC:Uniform distribution.

6. A continuous random variable X has probability density
function
f(x) =
0 if x< 0
x/4 if 0 < or = x< 2
1/2 if 2 < or = x< 3
0 if x> or = 3
(a) Find P(X<1)
(b) Find P(X<2.5)
(c) Find the cumulative distribution function F(x) = P(X< or
= x). Be sure to define the function for all real numbers x. (Hint:
The cdf will involve four pieces, depending on an interval/range
for x....

X is a continuous random variable with the cumulative
distribution function
F(x) = 0
when x <
0
= x2
when 0 ≤ x ≤
1
= 1
when x >
1
Compute P(1/4 < X ≤ 1/2)
What is f(x), the probability density function of X?
Compute E[X]

A random variable Y follows a continuous uniform distribution
from 0 to 4.
Express each question using proper
probability notation. Find probability by applying the area law
i.e. draw the distribution, mark the event, shade the area, find
the amount of shaded area.
What is the probability random variable Y takes a value less
than 3.2?
P[Y < 3.2] =
What is the probability random variable Y falls below 1.2?
P[Y < 1.2] =
What is the probability random variable...

a) Suppose that X is a uniform continuous random variable where
0 < x < 5. Find the pdf f(x) and use it to find P(2 < x
< 3.5).
b) Suppose that Y has an exponential distribution with mean 20.
Find the pdf f(y) and use it to compute P(18 < Y < 23).
c) Let X be a beta random variable a = 2 and b = 3. Find P(0.25
< X < 0.50)

1. A random variable X has a normal distribution with a mean of
75 and a variance of 9. Calculate P(60 < X < 70.5). Round
your answer to 4 decimal places.
2. A random variable X has a uniform distribution with a minimum
of -50 and a maximum of -20. Calculate P(X > -25). Round your
answer to 4 decimal places.
3.Which of the following statements about continuous random
variables and continuous probability distributions is/are TRUE?
I. The probability...

Let X be a continuous random variable with probability density
function (pdf) ?(?) = ??^3, 0 < ? < 2.
(a) Find the constant c.
(b) Find the cumulative distribution function (CDF) of X.
(c) Find P(X < 0.5), and P(X > 1.0).
(d) Find E(X), Var(X) and E(X5 ).

Let X represent a continuous random variable with a Uniform
distribution over the interval from 0 to 2. Find the following
probabilities (use 2 decimal places for all answers): (a) P(X ≤
1.92) = (b) P(X < 1.92) = (c) P(0.22 ≤ X ≤ 1.56) = (d) P(X <
0.22 or X > 1.56) =

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...

The continuous random variable X, has a uniform distribution
over the interval from 23 to 43. Given that z is a standard normal
random variable, what is the probability of z being greater than
-1.53? if the area to the left of z is 0.166, what is the value of
Z? if the area between this z and its negative value, –z is an area
of 0.97, what is the value of z?

A Uniform[0, 10] is a continuous random variable Y which assumes
any value between [0, 10] with equal chance, with density f(y) =
1/10 for all y ∈ [0, 10] and zero everywhere else. Check that it
satisfies the properties that a density function should have. Find
its distribution function F(y) for all y ∈ (−∞,∞) and show that it
satisfies the properties that a distribution function should
have.

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