Question

Let X be a discrete random variable with the range RX = {1, 2, 3, 4}. Let PX(1) = 0.25, PX(2) = 0.125, PX(3) = 0.125.

a) Compute PX(4).

b) Find the CDF of X.

c) Compute the probability that X is greater than 1 but less than or equal to 3.

Answer #1

a) It is known that

b) The cumulative density function of X is

c) The probability that X is greater than 1 but less than or equal to 3

Q6/
Let X be a discrete random variable defined by the
following probability function
x
2
3
7
9
f(x)
0.15
0.25
0.35
0.25
Give P(4≤ X < 8)
ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ
Q7/
Let X be a discrete random variable defined by the following
probability function
x
2
3
7
9
f(x)
0.15
0.25
0.35
0.25
Let F(x) be the CDF of X. Give F(7.5)
ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ
Q8/
Let X be a discrete random variable defined by the following
probability function :
x
2
6...

1. Let X be a discrete random variable with the probability mass
function P(x) = kx2 for x = 2, 3, 4, 6.
(a) Find the appropriate value of k.
(b) Find P(3), F(3), P(4.2), and F(4.2).
(c) Sketch the graphs of the pmf P(x) and of the cdf F(x).
(d) Find the mean µ and the variance σ 2 of X. [Note: For a
random variable, by definition its mean is the same as its
expectation, µ = E(X).]

The range of a discrete random variable X is {−1, 0, 1}. Let MX
(t) be the moment generating function of X, and let MX(1) = MX(2) =
0.5. Find the third moment of X, E(X^3).

The range of a discrete random variable X is {−1, 0, 1}. Let
MX(t) be the moment generating function of X, and let MX(1) = MX(2)
= 0.5. Find the third moment of X, E(X^3 )

Let X be a random variable with cdf ?(?) = 0 x<1
1/2(x^2)-x+3/4 1<=x<2
1 x>=2
(a) (1 pt) Find the median of X
(b) Find the pdf f(x)
(c) (1 pts) Find the variance of X.

1. A coin is tossed 3 times. Let x be the random discrete
variable representing the number of times tails comes up.
a) Create a sample space for the event;
b) Create a probability distribution table for the discrete
variable
x;
c) Calculate the expected value for x.
2. For the data below, representing a sample of times (in
minutes) students spend solving a certain Statistics problem, find
P35, range, Q2 and IQR.
3.0, 3.2, 4.6, 5.2 3.2, 3.5...

The following table lists the probability distribution of a
discrete random variable x:
x = 0,1,2,3,4,5,6,7
P(x) = 0.04, 0.11, 0.18, 0.22, 0.12, 0.21, 0.09, 0.03
a. The probability that x is less then 5:
b. The probability that x is greater then 3:
c. The probability that x is less than or equal ti 5:
d. The probability that x is greater than or equal to 4:
e. The probability that x assumes a value from 2 to 5:...

Problem 3. Let x be a discrete random variable with the
probability distribution given in the following table:
x = 50 100 150 200 250 300 350
p(x) = 0.05 0.10 0.25 0.15 0.15 0.20 0.10
(i) Find µ, σ 2 , and σ.
(ii) Construct a probability histogram for p(x).
(iii) What is the probability that x will fall in the interval
[µ − σ, µ + σ]?

Let X be a random variable with pdf f(x)=12,
0<x<2.
a) Find the cdf F(x).
b) Find the mean of X.
c) Find the variance of X.
d) Find F (1.4).
e) Find P(12<X<1).
f) Find PX>3.

Compute the mean and standard deviation of the random variable
with the given discrete probability distribution.
x
Px
−3
0.23
−2
0.15
7
0.25
9
0.27
10
0.1

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 6 minutes ago

asked 26 minutes ago

asked 33 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago